Datamatrix can refer to Matrix mathematics A rectangular array of elements Datamatrix statistics A matrix, generally of numbers, representing data used in statistical analysis Datamatrix computer An encoded barcode. Data set A collection of data in tabular form dab ... more details
refimprove date February 2010 Image Datamatrix.svg frame An example of a DataMatrix code, encoding the text Wikipedia, the free encyclopedia Image Semapedia.jpg thumb Reading DataMatrix code with mobile phone Semacode project Image Matrix 46.PNG thumb Marking surfaces A DataMatrix code is a two dimensional ... strength even if they are partially damaged, they can still be read. A DataMatrix symbol can store up to 2,335 alphanumeric characters. DataMatrix symbols are rectangular in shape and usually square ... a light module is a 0 and a dark module is a 1, or vice versa. Every DataMatrix is composed of two ... from 8 8 to 144 144. Applications Image STAMPIT Adresse.svg thumb Application of DataMatrix for Digital ... thumb Universal industrial code reader The most popular application for DataMatrix is marking small .... The DataMatrix is scalable, with commercial applications as small as 300 micrometres laser etched ... Industries Alliance EIA recommends using DataMatrix for labeling small electronic components. ref ... on the EIA website. DataMatrix codes are part of a new traceability drive in many industries ... serviceable parts. DataMatrix codes and accompanying alpha numeric data identify details of the component ... of Defense US Department of Defense has selected DataMatrix for the mandatory unique identification ... components of major systems must be permanently marked with a unique datamatrix code in accordance ... by DataMatrix codes within a tight deadline. ref http www.spec2000.com 50.html ATA Spec 2000 ref The Data ... DataMatrixDataMatrix symbols are made up of modules arranged within a perimeter finder and timing ... being the same as the background color. binary 0 . ECC200 is the newest version of DataMatrix ... when the symbol has sustained 30 damage, assuming the matrix can still be accurately located. Data ... aidc activities research.cfm ref DataMatrix applications Image Intelwireless datamatrix.jpg thumb A datamatrix on a Mini PCI card, encoding the serial number DataMatrix codes are becoming ... more details
wiktionarypar matrix TOCright Matrix may refer to Science and mathematics Matrix mathematics , a mathematical object generally represented as an array of numbers Matrix calculus , a notation for calculus operations on matrix spaces Identity matrix Similarity matrix , which scores the similarity between two data points A number of bioinformatic related matrices, including Position specific scoring matrix , which represents a pattern or motif in biological sequences Substitution matrix , which estimates ... over time PAM matrix , or Point Accepted Mutation matrix, used in scoring sequence alignments BLOSUM BLOcks of Amino Acid SUbstitution Matrix , also used in scoring sequence alignments Matrix biology ... or embedded Extracellular matrix , any material part of a tissue that is not part of any cell Mitochondrial matrix , the inner part of a mitochondrion, where the Krebs cycle takes place Osteon or bone matrix, a form of connective tissue found in bone Nuclear matrix , an insoluble fraction of the cell nucleus Germinal matrix , an embryonic brain tissue Matrix, another term for a bacterial growth medium Matrix archeology , the soil or sediment surrounding a dig site Harris matrix , an archaeological tool used to describe sediment deposition over time Matrix chemical analysis , the discarded portion of a sample used for chemical analysis Matrix geology , the fine grains between larger grains ... Matrix isolation , a continuous solid phase in which particles precipitates, etc. are embedded Metal matrix composite , a type of composite material Technology Multistate Anti Terrorism Information Exchange MATRIX , a database of US Citizens Matrix numismatics , an intermediate into which the design of a coin is engraved Matrix printing , a mold for shaping the letters Dot matrix , a type of printer or display, usually of text Matrix decoder , a technology which allows a finite number of audio channels to be decoded to a greater amount of audio channels i.e. Dolby or Quadraphonic Matrix or matrix ... more details
About the series The Matrix franchise other uses Matrix disambiguation Infobox film name The Matrix image The Matrix Poster.jpg caption Theatrical release poster director Andy Wachowski br Larry Wachowski ... by The Matrix Reloaded The Matrix is a 1999 science fiction film science fiction action film ... in the The Matrix series Matrix series of films, comic books, video games, and animation. The film ... this, computer programmer Neo The Matrix Neo is drawn into a rebellion against the machines, involving ... western s, dystopian fiction , and anime Japanese animation . Plot Computer programmer Neo The Matrix ... alias Neo. He wishes to learn the answer to the question What is the Matrix? based on cryptic messages on his computer. He encounters three sinister Agent The Matrix Agents , led by Agent Smith Hugo Weaving , which leads him to a group led by Morpheus The Matrix Morpheus Laurence Fishburne , who offers him the chance to learn the truth about the Matrix. Several members of Morpheus inner circle, including Trinity The Matrix Trinity Carrie Anne Moss , take Neo to a secret meeting, but only ... energy and body heat. The world in which Neo grew up was actually the Matrix, a simulated reality of the world ... and his crew belong to a group of free humans who unplug others from the Matrix and recruit them to their resistance against the machines. They are able to use their understanding of the Matrix s nature ... his limitless control over the Matrix. Neo is trained as a member of the rebellion. A socket in Neo s skull, used by the machines to connect him to the Matrix, also allows a direct connection to his ... arts styles. Further training introduces Neo to the key dangers in the Matrix itself. He learns that fatal ... any threats to the Matrix. Among their superhuman powers is the ability to take over the virtual body of anyone still directly connected to the Matrix. Morpheus is confident that once Neo fully ... the Matrix and takes Neo to meet the Oracle The Matrix Oracle Gloria Foster , the woman who has predicted ... more details
dablink For data in a computer science context, see Data computing . For other senses of the word, see Data disambiguation . See also datum , a disambiguation page. pp move indef Editors please keep the count mass discussion and etymology in the body, not the intro. The term data refers to qualitative or quantitative attributes of a variable mathematics variable or set of variables. Data plural of datum are typically the results of measurements and can be the basis of graph data structure graph s, image s, or observations of a set of variables. Data are often viewed as the lowest level of abstraction from which information and then knowledge are derived. Raw data , i.e. unprocessed data, refers ... that collect information to convert physical quantities into symbols. Etymology The word data pron ... . It is derived from ancient Persian word data . In discussions of problems in geometry , mathematics , engineering , and so on, the terms givens and data are used interchangeably. Also, data is a representation of a fact, figure, and idea. Such usage is the origin of data as a concept in computer science data are numbers, words, images, etc., accepted as they stand. Usage in English Weasel date ... data are measured. Any measurement or result is a datum , but data point is more common, ref cite ... . Both datums see usage in datum geodesy datum article and the originally Latin plural data are used as the plural of datum in English, but data is commonly treated as a mass noun and used with a verb ... the data from the experiment . This usage is inconsistent with the rules of Latin grammar and traditional English These are all the data from the experiment . Even when a very small quantity of data is referenced One number, for example the phrase piece of data is often used, as opposed to datum ... generic.xsl& publisher IEEE Computer Society ref allow usage of data as either a mass noun or plural ... data as a plural noun. For example, the Air Force Flight Test Center specifically states that the word ... more details
otheruses Data disambiguation Debt, AIDS, Trade, Africa or DATA was a multinational Non governmental organization non government organization founded in January 2002 in London by U2 s Bono along with Robert Sargent Shriver III Bobby Shriver and activist s from the Jubilee 2000 Drop the Debt campaign. DATA was created for the purpose of obtaining social equality equality and justice for Africa through debt relief , adjusting trade rules which burden Africa, eliminating the AIDS in Africa African AIDS epidemic, strengthening democracy , more accountability by the wealthiest nations and African leaders and Transparency humanities transparency towards the people. In 2007, DATA and Bono were jointly awarded the National Constitution Center s 2007 Liberty Medal for their groundbreaking efforts to address the AIDS crisis and extreme poverty in Africa. Start up funds came from the Bill & Melinda Gates Foundation , financier George Soros , and technology entrepreneur Edward W. Scott . ref cite news url http www.time.com time printout 0,8816,1142270,00.html title The Constant Charmer author Josh Tyrangiel date 2005 12 19 work Time Magazine ref In 2007, DATA and the ONE Campaign decided to join forces, and in January 2008, they formally merged under the name ONE. ref cite news url http www.reuters.com article idUSN2953856520071029 title Bono s U.S. based anti poverty groups to merge author Lesley Wroughton date 2007 10 29 work Reuters ref DATA received support from the Christian rock Alternative rock bands Switchfoot and Third Day . References references External links http www.one.org ONE official site Category International nongovernmental organizations Category HIV AIDS in Africa Category Organizations founded by Bono int org stub de Debt, AIDS, Trade in Africa it DATA vi DATA ... more details
The Matrix code can refer to A two dimensional barcode as opposed to linear and stacked symbologies , such as e.g. DataMatrix . The logo of The Matrix franchise. See Matrix digital rain . disambig ... more details
An irregular matrix , or ragged matrix , can be described as a matrix mathematics matrix that has a different number of elements in each row. Ragged matrices are not used in linear algebra , since standard matrix transformations cannot be performed on them, but they are useful as array data structure array s in computing . Irregular matrices are typically stored using Iliffe vector s. For example, the following is an irregular matrix math begin bmatrix 1 & 31 & 12& 3 7 & 2 1 & 2 & 2 end bmatrix math See also Regular matrix Sparse matrix References Paul E. Black, http www.nist.gov dads HTML raggedmatrix.html Ragged matrix , from Dictionary of Algorithms and Data Structures , Paul E. Black, ed., National Institute of Standards and Technology NIST , 2004. Category Arrays Category Matrices sl Nepravilna matrika ... more details
Infobox company company name Matrix Partners company logo Image Matrix Partners logo.png 175px Matrix ... Capital raised since inception ref homepage http www.matrixpartners.com www.matrixpartners.com Matrix ... , communications, semiconductors , data storage device data storage , Internet or wireless ..., China . Matrix Partners is not connected with Matrix Private Equity Partners LLP or Matrix Securities, which are part of Matrix Group, a UK financial services business based in London ref http www.matrixgroup.co.uk Matrix Group website ref . History Tracing its roots to 1977, Matrix was an active ... & Friedman . Among the firm s notable investments, Matrix Partners was an early stage investor in Apple ... Software , Vermeer Technologies Incorporated , and Xilinx . In 1985, Matrix raised its first institutional investor institutional private equity fund . Since then, Matrix has raised nine funds with total investor commitments of 2.4 billion. In 2001, Matrix Partners completed fundraising for Matrix ... 1bn fund for Matrix Partners . AltAssets, 2001 ref In 2006, Matrix raised Matrix Partners VIII fund ... ITM Matrix makes plans for 445m fund. Matrix Partners raises funds for its new fund Matrix Partners VIII . Private Equity Week, 2006 ref In 2006, Matrix also raised a separate 150 million India fund. ref http www.altassets.com news arc 2006 nz9161.php Matrix Partners closes India fund on 150m . AltAssets, 2006. ref ref http dealbook.blogs.nytimes.com 2006 08 03 matrix closes new india fund Matrix Closes New India Fund . New York Times, 2006 ref In July 2009, Matrix Partners raised Matrix IX ... . San Francisco Chronicle http www.thedeal.com techconfidential vc ratings matrix partners david skok pro.php Matrix Partners David Skok profits again this time from Tabblo . The Deal , 2007 http www.thefunded.com funds show Matrix Partners Matrix Partners Profile . The Funded http news.cnet.com 8301 13505 3 9914704 16.html Early Mozilla leader leaves Matrix Partners to rejoin the entrepreneurial ... more details
Advert date December 2007 O Matrix is a matrix programming language for mathematics , engineering , science , and financial analysis, marketed by Harmonic Software. The language is designed for High performance computing solutions. O Matrix is an integrated technical computing environment and matrix based scripting language. The O Matrix environment includes hundreds of mathematical, statistical, engineering and visualization functions. The diverse set of analysis functions enable the rapid development of complex, computationally intensive scientific, mathematical and engineering solutions. The O Matrix integrated environment provides a mode that is largely compatible with version 4 of the MATLAB language in the commercial product from MathWorks . More recent features of MATLAB , such as non numeric data types structures, cell arrays and objects , error handling with try catch, and nested and anonymous functions, are missing in O Matrix. The O Matrix environment includes a virtual machine of the O Matrix language to enable re distribution of solutions. External links http www.omatrix.com O Matrix site Harmonic Software . http www.scientificweb.com ncrunch ncrunch5.pdf Comparison of mathematical programs for data analysis ScientificWeb Category Array programming languages Category Numerical programming languages compu lang stub ... more details
In mathematics , computer science and graph theory , a distance matrix is a matrix mathematics matrix two dimensional array containing the distance s, taken pairwise, of a set of points. This matrix will have a size of N × N where N is the number of points, nodes or vertices often in a graph . Comparison with related matrices Comparison with Adjacency matrix Distance matrices are related to Adjacency matrix adjacency matrices , with the differences that a the latter only provides the information which vertices are connected but does not tell about costs or distances between the vertices and b an entry of a distance matrix is smaller if two elements are closer, while close connected vertices yield larger entries in an adjacency matrix. Comparison with Euclidean distance matrix Unlike a Euclidean distance matrix , the matrix does not need to be Symmetric matrix symmetric that is, the values x sub i,j sub do not necessarily equal x sub j,i sub . Similarly, the matrix values are not restricted to non negative Real number reals as they would be in the Euclidean distance matrix but rather can have negative values, zeros or imaginary number s depending on the cost metric and specific use. Although it is often the case, distance matrices are not restricted to being hollow matrix hollow that is, they can have non zero entries on the main diagonal. Examples and uses For example, suppose these data are to be analyzed, where pixel euclidean distance is the Metric mathematics distance metric . Image Clusters.svg frame none Raw data The distance matrix would be class wikitable ... 0 46 83 e 216 128 121 46 0 83 f 231 200 203 83 83 0 These data can then be viewed in graphic form ... NMR or X ray crystallography . Sometimes it is more convenient to express data as a similarity matrix . See also Data clustering Computer Vision Min plus matrix multiplication DEFAULTSORT Distance Matrix Category Metric geometry Category Bioinformatics Category Matrices mathapplied stub de Distanzmatrix ... more details
for other uses including the printer and display types, and fictional characters of this name Dot matrix disambiguation Image Dot matrix.svg right 300px A dot matrix is a 2 dimensional Array data structure array of dots used to represent characters, symbols and images. Typically the dot matrix is used in older computer printer s and many digital display device s. In printers, the dots are usually the darkened areas of the paper. In displays, the dots may light up, as in an light emitting diode LED or cathode ray tube CRT display, or darken, as in an liquid crystal display LCD , however multicolour LCDs are sometimes initially dark and light up. In the context of printers, the term mainly refers to computer printer Obsolete and special purpose printing technologies impact printer s, with a column of 8, 9 or 24 pins hitting an ink impregnated fabric ribbon, like a typewriter ribbon, onto the paper ... laser printer laser printing or inkjet printer inkjet printing , and are not called Dot Matrix printers. Dot Matrix printers survive where multi part forms are needed, as the impact can make a carbonless copy , for security purposes. A dot matrix is useful for marking materials other than paper. In manufacturing industry, many marking applications use dot matrix inkjet or impact methods. This can also be used to print 2D matrix codes, e.g. Datamatrix . Image Bling Bling Skywriting David Shankbone.jpg thumb Bling Bling Dot matrix style skywriting . In popular culture http reboot.wikia.com wiki Dot Matrix Dot Matrix is the name of a character on the acclaimed Computer generated imagery CGI show ReBoot . Dot Matrix is purposely named after the computer term. Dot Matrix is also the name of a character in the 1987 Mel Brooks film Spaceballs . See also Dot matrix display Dot matrix printer External ... Dot Matrix Printer Technology DEFAULTSORT Dot Matrix Category Digital imaging compu hardware stub it Dot matrix ... more details
For the notion in quantum mechanics, see scattering matrix In multivariate statistics and probability theory , the scatter matrix is a statistic that is used to make estimation of covariance matrices estimates of the covariance matrix of the multivariate normal distribution . Definition Given n samples of m dimensional data, represented as the m by n matrix, math X mathbf x 1, mathbf x 2, ldots, mathbf x n math , the sample mean is math overline mathbf x frac 1 n sum j 1 n mathbf x j math where math mathbf x j math is the j th column of math X , math . The scatter matrix is the m by m positive semi definite matrix math S sum j 1 n mathbf x j overline mathbf x mathbf x j overline mathbf x T math where math T math denotes matrix transpose . The scatter matrix may be expressed more succinctly as math S X ,C n ,X T math where math ,C n math is the n by n centering matrix . Application The maximum likelihood estimate, given n samples, for the covariance matrix of a multivariate normal distribution can be expressed as the normalized scatter matrix math C ML frac 1 n 1 S. math When the columns of math X , math are independently sampled from a multivariate normal distribution, then math S , math has a Wishart distribution . See also Estimation of covariance matrices Sample covariance matrix Wishart distribution Unreferenced date September 2010 DEFAULTSORT Scatter Matrix Category Multivariate statistics Category Matrices Statistics stub ... more details
When used as a data structure , the main alternative for the adjacency matrix is the adjacency list ...In mathematics and computer science , an adjacency matrix is a means of representing which vertices of a graph mathematics graph are adjacent to which other vertices. Another matrix representation for a graph is the incidence matrix . Specifically, the adjacency matrix of a finite set finite graph G on n vertices is the n × n matrix where the non diagonal entry a sub ij sub is the number of edges .... There exists a unique adjacency matrix for each isomorphism class of graphs up to permuting rows and columns , and it is not the adjacency matrix of any other isomorphism class of graphs. In the special case of a finite simple graph , the adjacency matrix is a 0,1 matrix with zeros on its diagonal. If the graph is undirected, the adjacency matrix is symmetric matrix symmetric . The relationship between a graph and the eigenvalue s and eigenvector s of its adjacency matrix is studied in spectral graph theory . Examples Here is an example of a labeled graph and its adjacency matrix. The convention followed here is that an adjacent edge counts 1 in the matrix for an undirected graph. X,Y coordinates are 1 6 class wikitable Labeled graph Adjacency matrix Image 6n graph2.svg 175px math ... & 1 1 & 1 & 0 & 1 & 0 & 0 0 & 0 & 0 & 1 & 0 & 0 end pmatrix math The adjacency matrix of a complete graph is all 1 s except for 0 s on the diagonal. The adjacency matrix of an empty graph is a zero matrix . Adjacency matrix of a bipartite graph Adjacency matrix of a bipartite graph & Biadjacency matrix redirect here The adjacency matrix A of a bipartite graph whose parts have r and s vertices has the form math A begin pmatrix O & B B T & O end pmatrix , math where B is an r × s matrix and O is an all zero matrix. Clearly, the matrix B uniquely represents the bipartite graphs, and it is commonly called its biadjacency matrix. Formally, let G U , V , E be a bipartite graph or bipartite graph ... more details
In mathematics , a Walsh matrix is a specific Matrix mathematics Square matrices and related definitions square matrix , with dimensions a power of 2, the entries of which are 1 or &minus 1, and the property that the dot product of any two distinct rows or columns is zero. The Walsh matrix was proposed by Joseph Leonard Walsh in 1923. ref name kanjilal Each row of a Walsh matrix corresponds to a Walsh function . The natural ordered Hadamard matrices Hadamard matrix is defined by the recursive formula below, and the sequency ordered Hadamard matrix is formed by rearranging the rows so that the number of sign changes in a row is in increasing order. ref name kanjilal Adaptive Prediction and Predictive Control, by P. P. Kanjilal, p 210, 1995, IET, ISBN 0863411932 ref Confusingly, different sources refer to either matrix as the Walsh matrix. The Walsh matrix and Walsh function s are used in computing the Walsh transform and have applications in the efficient implementation of certain signal processing operations. Formula The Hadamard matrices of dimension 2 sup k sup for k &isin N are given by the recursive formula The lowest order of Hadamard matrix is 2 math H 2 1 begin bmatrix 1 & 1 1 & 1 end bmatrix , math math H 2 2 begin bmatrix 1 & 1 & 1 & 1 1 & 1 & 1 & 1 1 & 1 & 1 & 1 1 & 1 & 1 & 1 end bmatrix , math and in general math H 2 k begin bmatrix H 2 k 1 & H 2 k 1 H 2 k 1 & H 2 k 1 end bmatrix H 2 otimes H 2 k 1 , math for 2 &le k &isin N , where math otimes math denotes the Kronecker product . Sequency ordering The sequency ordering of the rows of the Walsh matrix can be derived from the ordering of the Hadamard matrix by first applying the Cooley&ndash Tukey FFT algorithm Data reordering, bit reversal, and in place algorithms bit reversal permutation and then the Gray code permutation . ref Yuen, C. 1972. Remarks on the Ordering of Walsh ..., and 3 sign changes. See also Haar wavelet Quincunx matrix Notes reflist DEFAULTSORT Walsh Matrix Category ... more details
A matrix clock is a mechanism for capturing chronological and causal relationships in a distributed system . Matrix clocks are a generalization of the notion of vector clocks . ref name ParallelDrummond cite journal last1 Drummond first1 L cia M. A. last2 Barbosa first2 Valmir C. year 2003 title On reducing the complexity of matrix clocks journal Parallel Computing volume 29 issue 7 pages 895 905 doi 10.1016 S0167 8191 03 00066 8 ref A matrix clock maintains a Array data structure vector of the vector clocks for each communicating host. Every time a message is exchanged, the sending host sends not only what it knows about the global state of time , but also the state of time that it received from other hosts. This allows establishing a lower bound on what another hosts know, and is useful in applications such as checkpointing and Garbage collection computer science garbage collection . References reflist comp sci stub Category Distributed algorithms fr Horloge matricielle ... more details
In linear algebra , a Hankel matrix or catalecticant matrix , named after Hermann Hankel , is a square matrix with constant positive sloping skew diagonals, e.g. math begin bmatrix a & b & c & d & e b & c & d & e & f c & d & e & f & g d & e & f & g & h e & f & g & h & i end bmatrix . math In mathematical terms math a i,j a i 1,j 1 . , math The Hankel matrix is closely related to the Toeplitz matrix a Hankel matrix is an upside down Toeplitz matrix . For a special case of this matrix see Hilbert matrix . A Hankel operator mathematics operator on a Hilbert space is one whose matrix with respect to an orthonormal basis is an infinite Hankel matrix math a i,j i,j ge 1 math , where math a i,j math depends only on math i j math . The determinant of a Hankel matrix is called a catalecticant . Hankel transform The Hankel transform is the name sometimes given to the transformation of a sequence , where the transformed sequence corresponds to the determinant of the Hankel matrix. That is, the sequence math h n n ge 0 math is the Hankel transform of the sequence math b n n ge 0 math when math h n det b i j 2 1 le i,j le n 1 . math Here, math a i,j b i j 2 math is the Hankel matrix of the sequence math b n math . The Hankel transform is invariant under the binomial transform of a sequence. That is, if one writes math c n sum k 0 n n choose k b k math as the binomial transform of the sequence math b n math , then one has math det b i j 2 1 le i,j le n 1 det c i j 2 1 le i,j le n 1 . math Hankel ... data and a realization of an underlying state space or hidden Markov model is desired. The singular value decomposition of the Hankel matrix provides a means of computing the A, B, and C matrices which ... Hamburger moment problem Toeplitz matrix , a Hankel matrix upside down . References cite book title ... Matrices Category Transforms algebra stub de Hankel Matrix es Matriz de Hankel fr Matrice de Hankel it Matrice di Hankel nl Hankel matrix ru sl Hankelova matrika th ... more details
s and data structure s that take advantage of the sparse structure of the matrix. Operations using standard dense matrix structures and algorithms are slow and consume large amounts of Computer memory memory when applied to large sparse matrices. Sparse data is by nature easily data compression compressed , and this compression almost always results in significantly less computer data storage usage .... Storing a sparse matrix The na ve data structure for a matrix is a two dimensional array. Each entry in the array represents an element a sub i , j sub of the matrix and can be accessed by the two Index information technology indices i and j . For an m n matrix, enough memory to store at least m n entries to represent the matrix is needed. Substantial memory requirement reductions can be realised ...Image Finite element sparse matrix.png right thumb A sparse matrix obtained when solving a finite element ... of numerical analysis , a sparse matrix is a matrix mathematics matrix populated primarily ... had springs connecting each ball to all other balls, the system would be represented by a dense matrix ... , which have a low density of significant data or connections. Huge sparse matrices often appear ... entries, different data structures can be used and yield huge savings in Computer storage memory ... modification, and 2 those that support efficient matrix operations. The efficient modification group includes DOK, LIL, and COO and is typically used to construct the matrix. Once the matrix is constructed, it is typically converted to a format, such as CSR or CSC, which is more efficient for matrix ..., but poor for iterating over non zero values in sorted order. One typically creates the matrix with this format ... generated scipy.sparse.dok matrix.html scipy.sparse.dok matrix . List of lists LIL LIL stores ... sorted by column index for faster lookup. This is another format which is good for incremental matrix ... scipy.sparse.lil matrix . Coordinate list COO COO stores a list of code row, column, value code tuples ... more details
In statistics , a design matrix is a matrix mathematics matrix of explanatory variable s, often denoted by X , that is used in certain statistical models, e.g., the general linear model . ref Everitt,B.S. 2002 Cambridge Dictionary of Statistics , CUP. ISBN 0 521 91099 x ref ref George E. P. Box Box, G.E.P. , Tiao, G.C. 1973 Bayesian Inference in Statistical Analysis , Wiley. ISBN 0 471 57427 7 Section 8.1.1 ref It can contain indicator variable s ones and zeros that indicate group membership in an ANOVA . The design matrix represents the independent variable s in statistical models which describe observed data often called dependent variables in terms of other known variables explanatory variables . The theory relating to such models makes substantial use of matrix manipulations involving the design matrix see for example linear regression . A notable feature of the concept of a design matrix is that it is able to represent a number of different experimental designs and statistical models, e.g., ANOVA , ANCOVA , and linear regression . Example One way ANOVA Example with a one way analysis of variance ANOVA with 3 groups and 7 observations. The first column in the design matrix models the grand global mean of the y s, while the 3 remaining columns indicate the group membership of each observation. Here the first group consists of the 3 first observations and the next two groups each consist of two observations. math begin bmatrix y 1 y 2 y 3 y 4 y 5 y 6 y 7 end bmatrix begin bmatrix 1 & 1 &0 &0 1 &1 &0 &0 1 & 1 & 0 & 0 1 & 0 & 1 & 0 1 & 0 & 1 & 0 1 & 0 & 0 & 1 1 & 0 & 0 & 1 end bmatrix begin bmatrix mu tau 1 tau 2 tau 3 end bmatrix begin bmatrix u 1 u 2 u 3 u 4 u 5 u 6 u 7 end bmatrix math See also Hat matrix References references Category Matrices Category Regression analysis Category Statistical terminology ja ... more details
In mathematics , an incidence matrix is a matrix mathematics matrix that shows the relationship between two classes of objects. If the first class is X and the second is Y , the matrix has one row for each ... and oriented. The incidence matrix or unoriented incidence matrix of G is a p × q matrix math matrix ... math are incident and 0 otherwise. For example the incidence matrix of the undirected graph shown on the right is a matrix consisting of 4 rows corresponding to the four vertices and 4 columns corresponding ... end pmatrix math The incidence matrix of a directed graph D is a p × q matrix math b ij math where .... Note that many authors use the opposite sign convention. An oriented incidence matrix of an undirected graph G is the incidence matrix, in the sense of directed graphs, of any orientation of G ... difference, so one can speak of the oriented incidence matrix, even though that is technically incorrect. The oriented or unoriented incidence matrix of a graph G is related to the adjacency matrix of its line graph L G by the following theorem math A L G B G T B G 2I q math where math A L G math is the adjacency matrix of the line graph of G , B G is the incidence matrix, and math I q math is the identity matrix of dimension q. The Kirchhoff matrix is obtained from the oriented incidence matrix M G by the formula math M G M G T . math The integral cycle space of a graph is equal to the null space of its oriented incidence matrix, viewed as a matrix over the integers or real numbers ... matrix, viewed as a matrix over the two element field mathematics field . Signed and bidirected graphs The incidence matrix of a signed graph is a generalization of the oriented incidence matrix. It is the incidence matrix of any bidirected graph that orients the given signed graph. The column ... edge has either a 1 or a 1 in both rows. The line graph and Kirchhoff matrix properties generalize to signed graphs. Multigraph s The definitions of incidence matrix apply to graphs with loop graph theory ... more details
matrix multiplication , as well as the Hamming 7,4 encoding for error detection and recovery in data ...Unreferenced date December 2009 In the mathematics mathematical discipline of matrix theory , a block matrix or a partitioned matrix is a matrix mathematics matrix broken into sections called blocks . Looking at it another way, the matrix is written in terms of smaller matrices. We group the rows and columns ... and one bunch of adjacent columns. Rows and columns must be formed consistently the matrix is split into blocks by horizontal and vertical lines, which must cut the matrix completely in the given direction. The block matrix may also have an block matrix pseudoinverse inverse . Example File BlockMatrix168square.png thumb A 168 168 element block matrix with 12 12, 12 24, and 24 24 sub Matrices. Non zero elements are in blue, zero elements are grayed. The matrix math mathbf P begin bmatrix 1 & 1 ... end bmatrix . math The partitioned matrix can then be written as math mathbf P begin bmatrix mathbf P 11 & mathbf P 12 mathbf P 21 & mathbf P 22 end bmatrix . math Block Matrix Multiplication A block partitioned matrix product can be formed involving operations only on the submatrices. Given an math m times p math matrix math mathbf A math with math q math row partitions and math s math column ... A qs end bmatrix math and a math p times n math matrix math mathbf B math with math s math row ... mathbf B s1 & mathbf B s2 & cdots & mathbf B sr end bmatrix , math the matrix product math mathbf ... matrix with math q math row partitions and math r math column partitions. The matrices in your matrix ... matrix is a block matrix which is a square matrix , and having main diagonal blocks square matrices, such that the off diagonal blocks are zero matrices. A block diagonal matrix A has the form math ... 0 & 0 & cdots & mathbf A n end bmatrix math where A sub k sub is a square matrix in other words ... the latter being the same formalism used for a diagonal matrix . Any square matrix can trivially be considered ... more details
DISPLAYTITLE Morpheus The Matrix unsourced date July 2009 Infobox character colour black colour text white name Morpheus series The Matrix series The Matrix image caption first The Matrix last cause creator ... occupation title Captain of the List of ships in the Matrix series Nebuchadnezzar .28.22Neb.22.29 ... of a fictional character played by Laurence Fishburne in the science fiction films, The Matrix , The Matrix Reloaded , and The Matrix Revolutions . The Wachowski brothers , writers and directors of The Matrix films, were fans of Neil Gaiman and based the character of Morpheus on Dream comics ... date July 2008 also adopting one of his most common pseudonyms, Morpheus. Morpheus voice role in The Matrix ... Image of Morpheus from the Matrix In the Matrix films, Morpheus is the captain of the Nebuchadnezzar ship Nebuchadnezzar , which is a hovercraft of the human forces of the last human city, Zion The Matrix ... in the Matrix, a virtual computer generated world. Morpheus was once a human living inside the Matrix ... is also known in the Matrix fictional universe Matrix , but as a dangerous terrorism terrorist wanted by Agent The Matrix Agents , who appear to be Federal investigators but are sentient computer programs that patrol the Matrix, eliminating any threat to the Matrix. Like other hovercraft crews, Morpheus and his crew are dedicated to the protection of Zion and the freeing of humans from the Matrix ... s involvement with the dreaming of the Matrix. The mythical Morpheus and his family, including ... over to Morpheus in The Matrix, who offers Neo either a blue pill to forget about The Matrix and continue ... The One Earlier in his life, Morpheus gained the romantic attention of Niobe The Matrix Niobe ... The Matrix the Oracle , an ally living in the Matrix, who told Morpheus that he would be the person who would find Neo The Matrix the One , a human having superhuman abilities within the Matrix who ... the Matrix for the One. In the first feature film, The Matrix , Morpheus successfully finds and monitors ... more details
In statistics , the hat matrix , H , relates the fitted value s to the observed value s. It describes ... Matrix in Regression and ANOVA first1 David C. last1 Hoaglin first2 Roy E. last2 Welsch journal .... 32, No. 1 ref The diagonal elements of the hat matrix are the leverage statistics leverage s, which ... H mathbf y . math As is usually pronounced y hat , the hat matrix is so named as it puts a circumflex ... can be written as math mathbf y X boldsymbol beta boldsymbol varepsilon, math where X is a matrix of explanatory variable s the design matrix , is a vector of unknown parameters to be estimated, and ... y . math Therefore the hat matrix is given by math H X left X top X right 1 X top. math In the language of linear algebra , the hat matrix is the orthogonal projection onto the column space of the design matrix X . Note that math left X top X right 1 X top math is the Moore Penrose pseudoinverse Full rank pseudoinverse of X . The hat matrix corresponding to a linear model is symmetric matrix symmetric ... locally weighted scatterplot smoothing LOESS , for example, the hat matrix is in general neither ... using the hat matrix math mathbf r mathbf y mathbf hat y mathbf y H mathbf y I H mathbf y . math The covariance matrix of the residuals is therefore, by error propagation , equal to math left I H right top Sigma left I H right math , where &Sigma is the covariance matrix of the errors and by extension ... name Hoaglin1977 . For linear models , the trace linear algebra trace of the hat matrix is equal to the rank .... For other models such as LOESS that are still linear in the observations y , the hat matrix can be used ... of the model. The hat matrix has a number of useful algebraic properties. ref Gans, P. 1992 Data Fitting in the Chemical Sciences, , Wiley. ISBN 978 0 471 93412 7 ref ref Draper, N.R., Smith ... matrix in regression analysis include Leverage statistics leverage and Cook s distance , which are concerned ... matrix of the errors is &Sigma . Then since math hat boldsymbol beta left X top Sigma 1 X right ... more details
In mathematics and multivariate statistics , the centering matrix ref John I. Marden, Analyzing and Modeling Rank Data , Chapman & Hall, 1995, ISBN 0412995212, page 59. ref is a symmetric matrix symmetric and idempotent Matrix mathematics matrix , which when multiplied with a vector has the same effect as subtracting the mean of the components of the vector from every component. Definition The centering matrix of size n is defined as the n by n matrix math C n I n tfrac 1 n mathbb O math where math I n , math is the identity matrix of size n and math mathbb O math is an n by n matrix of all 1 s. This can also be written as math C n I n tfrac 1 n mathbf 1 mathbf 1 top math where math mathbf 1 math is the column vector of n ones and where math top math denotes matrix transpose . For example math C 1 begin bmatrix 0 end bmatrix math , math C 2 left begin array rrr 1 & 0 0 & 1 end array right frac 1 2 left begin array rrr 1 & 1 1 & 1 end array right left begin array rrr frac 1 2 & frac 1 2 frac 1 2 & frac 1 2 end array right math , math C 3 left begin array rrr 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 ..., it is zero and removing it again has no effect. math C n , math is singular matrix singular . The effects .... math C n , math has a kernel matrix nullspace of dimension 1, along the vector math mathbf 1 math . math C n , math is a projection matrix . That is, math C n mathbf v math is a projection of math mathbf .... Application Although multiplication by the centering matrix is not a computationally efficient ... of multiple vectors stored in the rows or columns of a matrix. For an m by n matrix math X , math , the multiplication ... math removes the means from each of the m rows. The centering matrix provides in particular a succinct way to express the scatter matrix , math S X mu mathbf 1 X mu mathbf 1 math of a data sample math X , math , where math mu tfrac 1 n X mathbf 1 math is the sample mean . The centering matrix allows us to express the scatter matrix more compactly as math S X ,C n X ,C n X ,C n ,C n ,X , X ,C n ,X ... more details
Z matrix may mean Z matrix chemistry , a table of the locations of atoms comprising a molecule Z matrix mathematics , a matrix whose off diagonal entries are less than or equal to zero It may also refer to The matrix of Z parameters , a matrix characterizing an electrical network disambig ... more details
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