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
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
The Matrix code can refer to A two dimensional barcode as opposed to linear and stacked symbologies , such as e.g. Data Matrix . The logo of The Matrix franchise. See Matrix digital rain . disambig ... more details
Matrix algebra may refer to Matrix theory , is the branch of mathematics that studies matrix mathematics matrices Matrix ring , thought of as an algebra over a field or a commutative ring disambig pl Algebra macierzy ... more details
In chemistry, matrix can refer to Matrix isolation , a technique which generally involves a reactive material being trapped within an unreactive solid matrix. Matrix chemical analysis , the remainder of the sample of which the analyte forms a part. dab ... more details
Merge from Matrix biology date May 2010 Unreferenced date December 2009 In biology , matrix plural matrices is the material or tissue between animal or plant cell biology cells , in which more specialized structures are embedded, and a specific part of the mitochondrion that is the site of oxidation of organic molecules. The internal structure of connective tissue s is an extracellular matrix . Finger nail s and toenail s grow from matrices. Tissue matrices Extracellular matrix Main Extracellular matrix The molecules forming the glue between cells in connective tissues are summarily referred to as the extracellular matrix. Bone matrix Main Osteon Bone is a form of connective tissue found in the body and has a storage area, or osteon region, also called matrix that allows mineral salts such as calcium to be stored. Subcellular matrices Mitochondrial matrix Main Mitochondrial matrix In the mitochondrion , the matrix contains soluble enzymes that catalysis catalyze the oxidation of pyruvic acid pyruvate and other small Organic chemistry organic molecule s. Nuclear matrix Main Nuclear matrix In the cell nucleus the matrix is the insoluble fraction that remains after extracting the solubled DNA . Golgi matrix The Golgi matrix is a protein scaffold made up of golgin s on the cytoplasm ic side of the Golgi apparatus involved in keeping its shape and membrane stacking. Matrix medium A matrix is also a Growth medium medium in which bacteria are grown cultured . For instance, a Petri dish of agar may be the matrix for culturing a sample swab bed from a patient s throat. See also Matrix biology Matricity Tissues and cells Germinal matrix Hair matrix cell Molecular biology Matrix protein Matrix metalloproteinase Matrix attachment region Bioinformatics and sequence evolution Similarity matrix PAM matrix Substitution matrix Position specific scoring matrix Botany and agriculture Matrix Planting Population biology and ecology Matrix population models DEFAULTSORT Matrix Biology Category ... more details
Regular matrix may refer to regular stochastic matrix , a stochastic matrix such that all the entries of some power of the matrix are positive. e.g. Lewis, Matrix Theory, p. 169 invertible matrix this usage is rare . e.g. Plato et al., Concise Numerical Algebra, p. 60 the opposite of irregular matrix , a matrix with a different number of entries in each row. mathdab ... more details
Data matrix can refer to Matrix mathematics A rectangular array of elements Data matrix statistics A matrix, generally of numbers, representing data used in statistical analysis Data matrix computer An encoded barcode. Data set A collection of data in tabular form dab ... more details
The Carver matrix can refer to CARVER matrix a military based target acquisition system Harris matrix Carver matrix Carver matrix seriation diagram named after Martin Carver which is designed to represent the time lapse in use of recognizable archaeological entities such as floors and pits. disambig ... more details
The term matrix model may refer to one of several concepts In theoretical physics , a matrix model is a system usually a quantum mechanics quantum mechanical system with matrix math matrix valued physical quantity physical quantities . See, for example, Lax pair . The old matrix models are relevant for string theory in two spacetime dimensions. The new matrix model is a synonym for Matrix theory physics Matrix theory . Matrix population models are used to model wildlife and human population dynamics. The Matrix Model of substance abuse treatment was a model developed by the Matrix Institute in the 1980 s to treat cocaine and methamphetamine addiction. A concept from Algebraic logic . The term Matrix model is used to describe Matrix management where each worker in an organisation has two managers, one functional managing their expertise, the other executive managing their work on an a project. disambig Category Mathematical disambiguation ... more details
Jacobi matrix may refer to Jacobian matrix and determinant of a smooth map between Euclidean space s or smooth manifold s Jacobi operator Jacobi matrix , a tridiagonal symmetric matrix appearing in the theory of orthogonal polynomials mathdab Long comment to avoid being listed on short pages ... more details
In mathematics , particularly matrix theory , a Stieltjes matrix , named after Thomas Joannes Stieltjes , is a real numbers real symmetric matrix symmetric positive definite Matrix mathematics matrix with nonpositive off diagonal entries. A Stieltjes matrix is necessarily an M matrix . Every n n Stieltjes matrix is invertible to a nonsingular symmetric matrix with nonnegative entries, though the converse of this statement is not true in general for n 2. From the above definition, a Stieltjes matrix is a symmetric invertible Z matrix mathematics Z matrix whose eigenvalues have positive real parts. As it is a Z matrix, its off diagonal entries are less than or equal to zero. See also Hurwitz matrix Metzler matrix References cite book title Iterative Solution of Large Linear Systems author David M. Young publisher Dover Publications date 2003 isbn 0486425487 page 42 cite book title Iterative Methods for Solving Linear Systems author Anne Greenbaum publisher Society for Industrial and Applied Mathematics SIAM date 1987 isbn 089871396X page 162 Category Matrices Category Numerical linear algebra maths stub Numerical linear algebra sl Stieltjesova matrika ... more details
Unreferenced stub auto yes date December 2009 In numismatics , a matrix is an intermediate used in the process of manufacturing coin s. A matrix has its design in the same sense as a Die manufacturing die . The design is engraved convex into the matrix, which is used to create punch numismatics punches . The matrix step was developed in the 17th century for two main reasons. The original design in the matrix could be better preserved, as a single matrix could be used to make several punches. Second, it made easier the addition of secondary details such as the legend, a difficult task DEFAULTSORT Matrix Numismatics Category Numismatics Coin stub it Matrice incisione ... more details
In linear algebra , the adjugate or classical adjoint of a square matrix is a matrix that plays a role similar to the invertible matrix inverse of a matrix it can however be defined for any square matrix ... is ambiguous. Today, adjoint of a matrix normally refers to its corresponding Hermitian ... ring and A is an n n matrix mathematics matrix with entries from R . The definition of the adjugate ... ij sub , as the determinant of the n 1 n 1 matrix that results from deleting ... ij 1 i j mathbf M ij . , math Define the Cofactor linear algebra Matrix of cofactors cofactor matrix of A , as the n n matrix C whose i , j entry is the i , j cofactor of A . The adjugate of A is the transpose of the cofactor matrix of A math mathrm adj mathbf A mathbf C T , math . That is, the adjugate of A is the n n matrix whose i , j entry is the j , i cofactor of A math mathrm adj mathbf A ij mathbf C ji , math . Examples 2 2 generic matrix The adjugate of the 2 2 matrix math mathbf ... & b c & a end pmatrix math . 3 3 generic matrix Consider the math 3 times 3 math matrix math mathbf ... matrix math mathbf C begin pmatrix left begin matrix A 22 & A 23 A 32 & A 33 end matrix right & left begin matrix A 21 & A 23 A 31 & A 33 end matrix right & left begin matrix A 21 & A 22 A 31 & A 32 end matrix right & & left begin matrix A 12 & A 13 A 32 & A 33 end matrix right & left begin matrix A 11 & A 13 A 31 & A 33 end matrix right & left begin matrix A 11 & A 12 A 31 & A 32 end matrix right & & left begin matrix A 12 & A 13 A 22 & A 23 end matrix right & left begin matrix A 11 & A 13 A 21 & A 23 end matrix right & left begin matrix A 11 & A 12 A 21 & A 22 end matrix right end pmatrix begin pmatrix left begin matrix 5 & 6 8 & 9 end matrix right & left begin matrix 4 & 6 7 & 9 end matrix right & left begin matrix 4 & 5 7 & 8 end matrix right & & left begin matrix 2 & 3 8 & 9 end matrix right & left begin matrix 1 & 3 7 & 9 end matrix right & left begin matrix 1 & 2 7 & 8 end matrix ... more details
distinguish matrix polynomial A polynomial matrix or sometimes matrix polynomial is a matrix mathematics matrix whose elements are univariate or multivariate polynomial s. A matrix is a matrix whose elements are polynomials in . A univariate polynomial matrix P of degree p is defined as math P sum n 0 p A n x n A 0 A 1 x A 2 x 2 cdots A p x p math where math A i math denotes a matrix of constant coefficients, and math A p math is non zero. Thus a polynomial matrix is the matrix equivalent of a polynomial, with each element of the matrix satisfying the definition of a polynomial of degree p . An example 3 3 polynomial matrix, degree 2 math P begin pmatrix 1 & x 2 & x 0 & 2x & 2 3x 2 & x 2 1 & 0 end pmatrix begin pmatrix 1 & 0 & 0 0 & 0 & 2 2 & 1 & 0 end pmatrix begin pmatrix 0 & 0 & 1 0 & 2 & 0 3 & 0 & 0 end pmatrix x begin pmatrix 0 & 1 & 0 0 & 0 & 0 0 & 1 & 0 end pmatrix x 2. math We can express this by saying that for a ring R , the rings math M n R X math and math M n R X math are Ring homomorphism isomorphic . Properties A polynomial matrix over a field mathematics field with determinant equal to a non zero element of that field is called unimodular matrix unimodular , and has an inverse, which is also a polynomial matrix. Note, that the only scalar unimodular polynomials ... degree is a rational function. The roots of a polynomial matrix over the complex numbers are the points in the complex plane where the matrix loses rank linear algebra rank . Note that polynomial matrices are not to be confused with monomial matrix monomial matrices , which are simply matrices with exactly ... field over which we constructed the matrix, by I the identity matrix, and we let A be a polynomial matrix, then the matrix I A is the characteristic matrix of the matrix A . Its determinant, I A is the characteristic polynomial of the matrix A . References E.V.Krishnamurthy, Error free Polynomial Matrix computations, Springer Verlag, New York, 1985 Category Matrices Category Polynomials ... more details
Context date October 2009 In matrix theory , the spread of a matrix describes how far apart the eigenvalues are in the complex plane . Suppose math A math is a square matrix with eigenvalues math lambda 1, ldots, lambda n math . Then the spread of math A math is the non negative number math s A max lambda i lambda j i,j 1, ldots n . math Examples For the zero matrix and the identity matrix , the spread is zero. Only math 0 math and math 1 math can be eigenvalues for a projection mathematics projection . A projection matrix therefore has spread math 0 math or math 1 math . All eigenvalues of an unitary matrix math A math lie on the unit circle . Hence math s A le 2 math . The spread of a matrix depends only on the spectral theory spectrum of the matrix, so if math B math is invertible matrix invertible , then math s A s BAB 1 . math See also Field of values References Marvin Marcus and Henryk Minc, A survey of matrix theory and matrix inequalities , Dover Publications , 1992, ISBN 0 486 67102 X. Chap.III.4. Category Linear algebra Category Matrix theory maths stub ... 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
Unreferenced date July 2009 In mathematics , and particularly ordinary differential equations , a monodromy matrix is the inverse of the fundamental matrix linear differential equation fundamental matrix of a system of ODEs evaluated at zero times the fundamental matrix evaluated at the period of the coefficients of the system. See also Monodromy Riemann Hilbert problem DEFAULTSORT Monodromy Matrix Category Ordinary differential equations math stub ... more details
Unreferenced date November 2006 In mathematics , a signature matrix is a diagonal matrix whose diagonal elements are plus or minus 1, that is, any matrix of the form math A begin pmatrix pm 1 & 0 & cdots & 0 & 0 0 & pm 1 & cdots & 0 & 0 vdots & vdots & ddots & vdots & vdots 0 & 0 & cdots & pm 1 & 0 0 & 0 & cdots & 0 & pm 1 end pmatrix math Any such matrix is its own inverse matrix inverse , hence is an involutary matrix . It is consequently a square root of a matrix square root of the identity matrix . Note however that not all square roots of the identity are signature matrices. Noting that signature matrices are both symmetric matrix symmetric and involutary, they are thus orthogonal matrix orthogonal . Consequently, any linear transformation corresponding to a signature matrix constitutes an isometry . Geometrically, signature matrices represent a reflection mathematics reflection in each of the axes corresponding to the negated rows or columns. See also Involution mathematics DEFAULTSORT Signature Matrix Category Matrices Maths stub sl Matrika oznak th ... more details
In mathematics , an Alexander matrix is a presentation matrix for the Alexander invariant of a knot mathematics knot . See also Alexander polynomial References Refimprove date June 2008 refbegin mathworld title Alexander matrix urlname AlexanderMatrix refend Category Knot theory topology stub ... 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 ..., 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 ranks . CNET, 2008 refend External links http www.matrixpartners.com Matrix Partners company website ... more details
In mathematics , especially in linear algebra and matrix theory , the commutation matrix is used for transforming the vectorized form of a matrix mathematics matrix into the vectorized form of its transpose . Specifically, the commutation matrix K sup m,n sup is the mn mn matrix which, for any m n matrix A , transforms vec A into vec A sup T sup K sup m,n sup vec A vec A sup T sup . Here vec A is the mn 1 column vector obtain by stacking the columns of A on top of one another vec A A sub 1,1 sub , ..., A sub m,1 sub , A sub 1,2 sub , ..., A sub m,2 sub , ..., A sub 1,n sub , ..., A sub m,n sub sup T sup where A A sub i,j sub . The main use of the commutation matrix, and the source of its name, is to commute the Kronecker product for every m n matrix A and every r q matrix B , K sup r,m sup A math otimes math B K sup n,q sup B math otimes math A . References Jan R. Magnus and Heinz Neudecker 1988 , Matrix Differential Calculus with Applications in Statistics and Econometrics , Wiley. math stub Category Linear algebra Category Matrices sl Komutacijska matrika ... more details
For the club in San Francisco The Matrix club Matrix is a club in Berlin which opened in 1996. Located at Warschauer Platz 18 in ten basement vaults of the Berlin Warschauer Stra e station Warschauer Stra e railway station , the discoth que houses up to nine bars and five dance floors. The venue is with an overall size of 2.100 square meters one of the biggest clubs in Berlin. Between 1996 and 2002 many international known discjockeys like Marusha , Chris Isaac , Westbam , Underground Resistance , Josh Wink , Lords of the Underground , Lady B , Sven V th , Paul van Dyk and other exponents of electronic music performed in the Matrix. Since 2003 the programming is enlarged. Artists who have performed in recent years are Sabrina Setlur , Ne Yo , Georges Morel , Vibe Kingz , DJ Size and others. About three years the club had an own truck at the Berlin Love Parade . The venue is also used for showcases and filmsets. External links http www.matrix berlin.de Official Matrix Berlin website coord missing Germany Category Nightclubs in Germany Matrix Club Category Music in Berlin Matrix Club da Matrix club de Matrix Club fr Matrix club no Matrix klubb sv Matrix nattklubb ... more details
distinguish Polynomial matrix In mathematics, a matrix polynomial is a polynomial with matrix mathematics matrices as variables. Examples include math P A sum i 0 n a i A i a 0 I a 1 A a 2 A 2 cdots a n A n, math where P is a polynomial, math P x sum i 0 n a i x i a 0 a 1 x a 2 x 2 cdots a n x n, math and I is the identity matrix. math left A,B right A B B A, math the commutator Ring theory commutator of A and B . A matrix polynomial equation is an equality between two matrix polynomials, which holds for the specific matrices in question. If math P A Q A math , where A is a matrix over a field , then the eigenvalues of A satisfy the characteristic equation Disputed inline Characteristic equation date October 2010 math P lambda Q lambda math . br A matrix polynomial identity is a matrix polynomial equation which holds for all matricies A in a specified matrix ring M sub n sub R . DEFAULTSORT Matrix Polynomial Category Matrices Category Polynomials algebra stub ... more details
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