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  1. Decimal representation

    This article gives a mathematical definition. For a more accessible article see Decimal . A decimal representation of a non negative real number r is an expression of the form of a series mathematics series , traditionally written as a sum math r sum i 0 infty frac a i 10 i math where a sub 0 sub is a nonnegative ... sub     9, called the digits of the decimal representation. The sequence of digits specified ... Algorithms publisher Addison Wesley year 1973 pages 21 ref This restriction still allows a decimal representation for each non negative real number, but additionally makes such a representation unique. The number defined by a decimal representation is often written more briefly as math r a 0.a ... decimal representation is easily established. Non uniqueness of decimal representation Main 0.999... Some real numbers have two infinite decimal representations. For example, the number 1 may be equally ... s inverter tries to identify a number given the start of its decimal representation. For instance ... decimal representations with an infinite sequence of digits  9. ref citation last Knuth first ... sum i 0 n frac a i 10 i math . Finite decimal approximations Any real number can be approximated to any desired degree of accuracy by rational number s with finite decimal representations. Assume math x geq 0 math . Then for every integer math n geq 1 math there is a finite decimal math r n ... the infinite sequence of zero digits, removing any final zero digits and a possible final decimal point, a normalized finite decimal representation is obtained. Citation needed date November 2009 Finite decimal representations The decimal expansion of non negative real number x will end in zeros ... sup m sup , where m and n are non negative integers. Proof If the decimal expansion of x will end in zeros ... in zeros. Recurring decimal representations Main Repeating decimal Some real numbers have decimal ... as a ratio of a non negative and a positive integer . See also Decimal Series mathematics IEEE ...   more details



  1. Decimal

    aims to be an accessible introduction. For the mathematical definition, see Decimal representation . Table Numeral Systems The decimal numeral system also called base ten or occasionally denary has ... of the fact the recurring part of a decimal representation is, in fact, an infinite ... numbers further Decimal representation Every real number has a possibly infinite decimal representation ... recurring decimal representation. Non uniqueness of decimal representation Consider those rational ... sup a sup 5 sup b sup . In this case there is a terminating decimal representation. For instance, 1 ... 1.0448. Such numbers are the only real numbers which do not have a unique decimal representation, as they can ... representations neither terminate nor recur. So in general the decimal representation is unique ... base numeration systems, such as golden mean base representation. Decimal computation Decimal computation ... decimal representation internally . ref Fingers or Fists? The Choice of Decimal or Binary Representation ... coded decimal Decimal representation Decimal separator Dewey Decimal System Hindu Arabic numeral system ... Harding, Sophie Wood and Ian Monk ref Decimal notation often refers to a base 10 positional notation ... of ten. Decimals also refer to decimal fractions, either separately or in contrast to Vulgar fraction vulgar fractions . In this context, a decimal is a tenth part, and decimals become a series of nested tenths. There was a notation in use like tenth metre , meaning the tenth decimal of the metre, currently an Angstrom. The contrast here is between decimals and vulgar fractions, and decimal divisions and other divisions of measures, like the inch. It is possible to follow a decimal expansion ... of decimals, followed by a trinary place. Decimal notation Decimal notation is the writing of number ... have symbols for the decimal powers 1, 10, 100, 1000 and secondary symbols for half these values ... use Hindu Arabic numerals speak of decimal notation, they often mean not just decimal numeration ...   more details



  1. Representation

    Wiktionarypar representation represent Representation can refer to Representation politics , one s ability to influence the political process Representative democracy Permanent Representation, a type of Diplomatic mission Representation of the International NGO the representative office of the International non governmental organization INGO mission Representation arts , the depiction and ethical concerns of construction in visual arts and literature. Depiction is meaning conveyed through pictures Representation psychology , a hypothetical internal cognitive symbol that represents external reality Representation mathematics and group representation Multiple representations mathematics education Representation chemistry Representation systemics Knowledge representation , the study of formal ways to describe knowledge Legal representation or advocacy is provided by lawyers Lobbying for a group of individuals or companies In unionised workplaces, Union steward shop stewards and union executives can represent employees The legal status of a statement made with regards to Contract Contract Law Represent can refer to Represent Fat Joe album Represent Fat Joe album , a 1993 album by Fat Joe Represent Compton s Most Wanted album Represent Compton s Most Wanted album , a 2000 album by Compton s Most Wanted Represent , a 1994 album by DJ Magic Mike Represent song Represent song , a song by Nas Represent , a 2009 song by The Red Jumpsuit Apparatus Represent Weezer song Represent , a 2010 single by Weezer released as an unofficial anthem for the United States men s national soccer team See also disambig cs Reprezentace de Repr sentation es Representaci n fr Repr sentation homonymie nl Representatie pt Representa o ru simple Representation fi Representaatio sv Representation ...   more details



  1. Serial decimal

    orphan date November 2006 In computers, a serial decimal numeric representation is one in which ten bit s are reserved for each digit, with a different bit turned on depending on which of the ten possible digits is intended. ENIAC used this representation. ref http www.tjhsst.edu prittman arch Chap1 Chap1Old.html tjhsst.edu ref References reflist Category Computer arithmetic compu storage stub ...   more details



  1. Decimal degrees

    the earth is a oblate spheroid . Example The decimal degree representation of the location of the United ...Decimal degrees DD express latitude and longitude Geographic coordinate system geographic coordinates as decimal fractions and are used in many Geographic information system Geographic Information Systems GIS , web mapping applications such as Google Maps , and Global Positioning System GPS devices. Decimal degrees are an alternative to using degrees, minutes, and seconds DMS . As with latitude and longitude, the values are bounded by 90 and 180 each. Positive latitudes are north of the equator, negative latitudes are south of the equator. Positive longitudes are east of Prime Meridian , negative longitudes are west of the Prime Meridian. Latitude and longitude are usually expressed in that sequence, latitude before longitude. Accuracy The radius of the semi major axis of the Earth at the equator is 6,378,160.0 meters ref http www.ga.gov.au geodesy datums agd.jsp Australian Geodetic Datum ref resulting in a circumference of 40,075,161.2 meters. The equator is divided into 360 degrees of longitude, so each degree at the equator represents 111,319.9 metres or approximately 111  km. As one moves away from the equator towards a pole, however, one degree of longitude represents a diminishing number of meters, approaching zero at the pole. The number of decimal places required for a particular accuracy at the equator is class wikitable Accuracy versus decimal places decimal br places ...  mm A value in decimal degrees to an accuracy of 4 decimal places is accurate to 11.1 meters 5.55 m at the equator . A value in decimal degrees to 5 decimal places is accurate to 1.11 meter at the equator ... DMS value is converted to decimal degrees using the formula decimal D M 60 S 3600 The decimal degree representation for the location of the United States Capitol of 38 53 23 N, 77 00 32 W is 38.889722 , 77.008889 References reflist DEFAULTSORT Decimal Degrees Category Geographic information systems ...   more details



  1. Decimal (disambiguation)

    Wiktionarypar decimal Decimal could mean The decimal or base ten numeral system Decimal unit , an obsolete unit of measure in India and Bangladesh Decimal separator , used to mark the boundary between the ones and tenths place in numbers e.g. 12.4 , often referred to as a decimal disambig ...   more details



  1. Decimal time

    Refimprove date July 2009 Decimal time is the representation of the time of day using units which are decimal ... , which divides the day into 10 decimal hours, each decimal hour into 100 decimal minutes and each decimal minute into 100 decimal seconds, as opposed to the more familiar standard time , which divides ... republicaine1.jpg right thumb 200px French decimal clock from the time of the French Revolution History China Main Ke unit Decimal time was used in China throughout most of its history alongside duodecimal ... each fen into 100 miao , creating a complete decimal time system of 100 ke , 100 fen and 100 ... across cultures Dordrecht Kluwer, 2000 373 407, p.393, ISBN 0 7923 6481 3. ref Chinese decimal time ... modern times, decimal time was introduced during the French Revolution in the decree of 5 October ... part of the hour is called decimal minute the hundredth part of the minute is called decimal second ... es were produced with faces showing both standard time with numbers 1 24 and decimal time with numbers 1 10, decimal time never caught on it was not officially used until the beginning of the Republican ..., as the metric time unit. Decimal time was introduced as part of the French Republican Calendar , which ... Observatory . Decimal time would also have been reckoned according to apparent solar time, depending ... into 100 decimal minutes, and each minute into 100 seconds. The plan did not gain acceptance and was abandoned ... definition of the standard second in a standard day, but in the French decimal time system there are 100,000 decimal seconds in the day, so the decimal second is shorter than its counterpart. class wikitable border 1 Decimal unit Seconds Minutes Hours h mm ss Decimal second 0.864 0.0144 0.00024 0 00 00.9 Decimal minute 86.4 1.44 0.024 0 01 26.4 Decimal hour 8,640 144 2.4 2 24 00.0 Fractional days The most common use of decimal time of day is as fractional days used by scientist s and computer programmer ... elapsed since midnight by 24 to make a Decimal Decimal fractions decimal fraction . Thus, midnight ...   more details



  1. Decimal mark

    , Esperanto , also uses the comma as its official decimal mark. In 1958, disputes between European and American delegates over the correct representation of the decimal mark nearly stalled the development ...Selfref For the proper choice of the decimal mark in English language Wikipedia articles, see Wikipedia Manual of Style Decimal separator . Numeral systems Different symbols have been and are used for the decimal mark . The choice of symbol for the decimal mark affects the choice of symbol for the thousands .... The decimal mark is mathematically a radix point . The English term decimal is limited to base ten, but the separator in non decimal numeral system s may be referred to as a radix point . In a binary ... part, a tradition derived from the decimal system used in Indian mathematics . ref Reimer, L ... a decimal point. Later, a separator unicode a short, roughly vertical, ink stroke between the units ... the decimal units position, such as Italy , for example. ref Enciclopedia Universal Santillana ... en los n meros no enteros para separar la parte entera de la parte decimal o fraccionaria p.ej. ... is called a stop or full stop in other countries, was used as the standard decimal mark. In the nations ... mid dot , which can also be called an interpunct often referred to as the decimal point was preferred for the decimal mark in printing technologies that could accommodate it. ref Reimer, L. and Reimer ... to indicate multiplication, the SI rejected its use as the decimal mark. However, the use of the period as decimal mark was not banned. British aviation magazines thus switched to the US form in the late twentieth century. When South Africa adopted the metric system , it adopted the comma as its decimal ... as its decimal mark since the publication of the Interlingua A Grammar of the International Language ... of ALGOL , ACM SIGPLAN Notices, August 1978. ref ALGOL ended up allowing different decimal marks ... on Weights and Measures declared in 2003 that the symbol for the decimal marker shall be either ...   more details



  1. Repeating decimal

    A decimal representation of a real number is called a repeating decimal or recurring decimal if at some ... indefinitely. For example, the decimal representation of nowrap 1 3 0.3333333... spoken as 0.3 repeating , or 0.3 recurring becomes periodic just after the decimal point, repeating the single digit ... the decimal representation becomes periodic at the second digit after the decimal point, repeating the sequence of digits 144 infinitely. A real number has an ultimately periodic decimal representation ... hand, the decimal representation of a rational number is ultimately periodic because it can ..., whose solution is nowrap 58086 9990 3227 555. A decimal representation written with a repeating ... decimal representation. Background Notation One convention to indicate a repeating decimal is to put ... integers coprime to 10 If p is a prime other than 2 or 5, the decimal representation of the fraction ... sup T sub p sub If p and q are primes other than 2 or 5, the decimal representation of the fraction .... On the other hand, each repeating decimal number satisfies a linear equation with integral coefficients ..., 2nd ed. Oxford, England Oxford University Press, 1996 p. 67 . ref The decimal is also called a terminating decimal . Terminating decimals represent rational number s of the form k 2 sup n sup 5 sup m sup . For example, nowrap 1.585 317 200 317 2 sup 3 sup 5 sup 2 sup . A terminating decimal can be written as a decimal fraction nowrap 317 200 1585 1000 . However, a terminating decimal also has a representation as a repeating decimal, obtained by decreasing the final nonzero digit by one and appending ...... are two examples of this. A decimal that is neither terminating nor repeating represents ... Decimal expansion and recurrence sequence In order to convert a rational number represented as a fraction into decimal form, one may use long division . For example, consider the rational number 5 ... began with. Therefore the decimal repeats   0.0675  675  675  .... Every rational number ...   more details



  1. Decimal system

    Decimal system may refer to The decimal base ten number system, used in mathematics for writing numbers and performing arithmetic. The Dewey Decimal Classification Dewey Decimal System , a subject classification system used in libraries. The decimal currency system, where each unit of currency can be divided into 100 sub units. Disambig nl Decimale stelsel ...   more details



  1. Decimal computer

    orphan date August 2009 Decimal computers represent numbers and or addresses in decimal , and provide instructions to operate on those numbers and or addresses directly examples of encoding used are Binary coded decimal BCD , Excess 3 , two out of five code , ASCII , and EBCDIC . Many early computer s, for example the ENIAC , IBM 702 , IBM 705 , IBM 650 , IBM 1401 , IBM 1620 , IBM NORC , IBM 7070 , IBM 7080 , UNIVAC I , UNIVAC II and UNIVAC III used decimal arithmetic IBM 1401 addresses were a combination of decimal and binary arithmetic . Later, several microprocessor s offered limited decimal support. For example, the 80x86 family of microprocessors provide instructions to convert one byte Binary coded decimal BCD numbers packed and unpacked to Binary file binary format before or after arithmetic operations ref cite web title MASM Programmer s Guide publisher Microsoft date 1992 url http webster.cs.ucr.edu Page TechDocs MASMDoc ProgrammersGuide Chap 06.htm doi accessdate 2007 07 01 ref . These operations were not extended to wider formats and hence are now slower than using 32 bit or wider BCD tricks to compute in BCD see http www.cs.uiowa.edu jones bcd bcd.html . The Motorola 68000 68000 provided instructions for BCD addition and subtractions ref cite web title Motorola M68000 Family Programmer s Reference Manual url http www.freescale.com files archives doc ref manual M68000PRM.pdf .... need refs to s 360, 370, etc., here Decimal arithmetic is now becoming more common for instance, three decimal floating point types with two encodings have been added to the new IEEE 754r IEEE 754 standard, with 7, 16, and 34 digit decimal significand s. ref cite web title DRAFT Standard for Floating ... z10 have implemented these types using the Densely Packed Decimal scheme for encoding the digits ... Decimal Arithmetic publisher IBM url http speleotrove.com decimal accessdate 2008 04 08 ref , the first and third in hardware and the second in microcode. References references br DEFAULTSORT Decimal ...   more details



  1. Decimal Birthday

    Refimprove date February 2008 Original research date February 2008 A decimal birthday is celebrated using the decimal base ten numeral system . Decimal birthdays can be celebrated using any time unit years, months, days, hours, minutes, seconds , however the most common form of celebration uses days. The main form of celebration falls on the occurrence of every 1000th day of a person s life. The standard practise is to count the day of birth as day zero and then count upwards from that day onwards. This form of celebration has become more popular since the widespread use of computers and the internet which have made the calculation of the decimal birthday easier to make. However, the celebration of a decimal birthday has some traditional significance in some cultures, for example in Korea it is common to celebrate the Bek Il or the 100th day of life ref http www.asianinfo.org asianinfo korea cel birthday celebrations.htm ref . This tradition was born from a time of high infant mortality when many babies would die before three months of age. As a result the 100th day is a celebration of life as the baby has survived the difficult first 100 days of life. In western society the celebration of the 10,000th day of life, although still practiced by a minority, is a phenomenon that has been recorded in several countries including the United Kingdom and Australia. The 10,000th day of life occurs between the 27th and 28th year of life and as a consequence can be noticed by young professionals, especially those in industries that rely on a strong mathematical knowledge. Decimal birthdays should not be confused with decimal time which instead of applying the decimal system to current measures of time days, hours, minutes etc. instead changes the measurement of time itself into a decimal system. References Reflist added above External links Sources by script assisted edit External links http www.tkday.com TKDay http www.jarusa.com birthday Decimal Birthday Category Birthdays culture ...   more details



  1. Decimal Dozen

    Image Decimal dozen.jpg thumb Decimal dozen A decimal dozen is a design of carton s for bottled wine that holds two rows of five bottles, developed by the Helm Wines winery , Canberra , Australia , to replace traditional dozen bottle cartons. The quoted motivation is that demographics reports show that females buy more than 50 percent of wine in Australia. According to the OH&S regulations, a female should not lift more than 15 kilogram s 33 lbs , which is only the minimum gross weight of a standard 12 bottle carton, which can weigh up to 20 kg for some types of bottles. ref http direct.bl.uk bld PlaceOrder.do?UIN 119109620&ETOC RN&from searchengine Decimal dozen for the female touch , Australian and New Zealand Grapegrower and Winemaker , 2002, issue 464. ref In 2005 it was a nominee for the Australian Capital Territory ACT Occupational Health and Safety Award in the category Best Solution to an Identified Workplace Health and Safety Issue for addressing the manual handling issues by introducing a ten bottle carton in a 2 X 5 configuration . ref http www.workcover.act.gov.au pdfs promotions Nominees 05.pdf ACT Occupational Health & Safety Awards 2005 Nominees ref See also Baker s dozen Decimal inch References reflist Category Packaging Category Wine packaging and storage wine stub ...   more details



  1. Decimal (unit)

    A decimal also spelled decimel is an obsolete unit of area in India and Bangladesh approximately equal to 1 100 acre 40.46  m . After metrication in the mid 20th century by both countries, the unit became obsolete. See also List of customary units of measurement in South Asia References cite web url http www.sizes.com units decimal.htm title Decimal accessdate 2007 02 19 work http www.sizes.com indexes.htm Sizes, grades, units, scales, calendars, chronologies Category Customary units in India Category Obsolete units of measure Category Units of area measurement stub ...   more details



  1. Decimal Day

    for rationale Decimal Day 15 February 1971 was the day the United Kingdom and Republic of Ireland ... of the pound sterling Pre decimal coinage Under the old currency of pound sterling pounds , Shilling ... computer use, monetary calculation, such as adding up sums of money, was more complicated than with a decimal ... penny coin pre decimal penny , with the same diameter as the Half dollar United States coin U.S. half ... in 1795 of the decimal French franc , little practical progress towards decimalisation was made ... in that direction but failed to gain acceptance and was struck only from 1887 to 1890. The Decimal ... that the florin was issued. In their preliminary report, the Royal Commission on Decimal ... conclusion about the adoption of any such scheme. ref Royal Commission on Decimal Coinage. http www.bopcris.ac.uk ... Final Report of the Decimal Coinage Commissioners . ref In 1862, the Select Committee Westminster ... now sits in the House of Lords . The Royal Commission on Decimal Coinage 1918 20 , chaired by Alfred ... pound . ref Royal Commission on Decimal Coinage http www.bopcris.ac.uk bopall ref7833.html Decimal ... of decimalisation in South Africa, prompted the Government to set up the Committee of the Inquiry on Decimal ... in the report was announced on 1 March 1966. The Decimal Currency Board DCB was created to manage the transition, although the plans were not approved by Parliament until the Decimal Currency Act 1969 Decimal Currency Act in May 1969. Former Greater London Council leader Bill Fiske was named as the Chairman of the Decimal Currency Board. Consideration was given to having a new unit of currency ... in the old currency which would have resulted in the decimal penny being worth only slightly ... that had to be introduced on Decimal Day and meant that the public was already familiar with three ... programmes, Decimal Five , to which The Scaffold contributed some specially written tunes. ITV repeatedly ... and after. Prior to Decimal Day the double pricing was displayed as e.g. 1s 5p from Decimal Day the order ...   more details



  1. Decimal calendar

    Unreferenced date April 2009 A decimal calendar contains either ten days per week, a multiple of ten days in a month, or ten months per year. Examples that have been adopted are the Roman calendar calendar of Romulus , the Egyptian calendar , the Alexandrian calendar , the Coptic calendar , the Ethiopian calendar , and the French Republican Calendar . Calendar of Romulus The only calendar with a ten month year was the Roman calendar calendar of Romulus adopted sometime after Romulus and Remus founded the city of Rome in 753 BC, when Romulus killed Remus. According to Roman writers, including Censorinus and Macrobius , it had ten of the twelve months in our modern calendar, March through December, but it only had 304 days in its year. The remaining days needed to form a solar year were winter days not assigned to any month. It only lasted until about 700 BC when King Numa Pompilius Numa , the successor of Romulus, added the winter months of January and February and rearranged the number of days in each month, creating the Roman calendar . Egyptian, Alexandrian, Coptic, and Ethiopian calendars The Egyptian calendar of the first three millennia BC had twelve months of 30 days each, consisting of three ten day weeks, plus five epagomenal days at the end of the year. The Alexandrian calendar, named for the city of Alexandria , is the Egyptian calendar with an additional sixth epagomenal or leap day added to the end of the year, as decreed in 25 BC by the Roman emperor Augustus five years after he conquered Egypt . The Coptic calendar is the Alexandrian calendar as adopted by the Coptic Orthodox Church of Alexandria Coptic Church at the beginning of the fourth century. The Ethiopian calendar is the Alexandrian calendar as adopted by the Ethiopian Church during the fourth century ... Republican Calendar, which was introduced along with decimal time in 1793, was a modern version ... day weeks or ten month years, so a few decimal calendars have been proposed by individuals to create ...   more details



  1. Symbolic representation

    Symbolic representation may refer to Symbolism disambiguation Symbolic linguistic representation See also Symbolic disambiguation Representation disambiguation disambig ...   more details



  1. Permutation representation

    In mathematics , permutation representation may refer to A group action . Permutation representation symmetric group disambiguation ...   more details



  1. Complex representation

    The term complex representation has slightly different meanings in mathematics and physics. In mathematics , a complex representation is a group representation of a group or Lie algebra on a complex vector space. In physics , a complex representation is a group representation of a group or Lie algebra on a complex vector space that is neither real representation real nor pseudoreal representation pseudoreal . In other words, the Group mathematics group elements are expressed as complex matrices, and the complex conjugate of a complex representation is a different, non equivalent representation. For compact groups, the Frobenius Schur indicator can be used to tell whether a representation is real, complex, or pseudo real. For example, the N dimensional fundamental representation of SU N for N greater than two is a complex representation whose complex conjugate is often called the antifundamental representation . algebra stub Category Representation theory of groups ...   more details



  1. Antifundamental representation

    In mathematics , an antifundamental representation is the complex conjugate of the fundamental representation , although the distinction between the fundamental and the antifundamental representation is a matter of convention. However, these two are often non equivalent, because each of them is a complex representation . Category Representation theory of Lie groups geometry stub ...   more details



  1. Bifundamental representation

    In mathematics and theoretical physics , a bifundamental representation is a representation theory representation obtained as a tensor product of two fundamental representation fundamental or antifundamental representation antifundamental representations. For example, the MN dimensional representation M , N of the group math SU M times SU N math is a bifundamental representation. These representations occur in quiver diagram s. algebra stub Category Abstract algebra ...   more details



  1. Adjoint representation

    The adjoint representation can refer to Ad the adjoint representation of a Lie group G ad the adjoint representation of a Lie algebra math mathfrak g math , see adjoint endomorphism . mathdab ...   more details



  1. Monomial representation

    In mathematics , a linear representation &rho of a group G is a monomial representation if there is a finite index subgroup H and a one dimensional linear representation &sigma of H , such that &rho is equivalent to the induced representation Ind sub H sub sup G sup &sigma . Alternatively, one may define it as a representation whose image is in the monomial matrices . Here for example G and H may be finite group s, so that induced representation has a classical sense. The monomial representation is only a little more complicated than the permutation representation of G on the coset s of H . It is necessary only to keep track of scalars coming from &sigma applied to elements of H . References Springer id m m064780 title Monomial representation Category Representation theory of groups it Rappresentazione monomiale ...   more details



  1. Quasiregular representation

    Unreferenced date December 2009 Orphan date December 2009 This article addresses the notion of quasiregularity in the context of representation theory and topological algebra . For other notions of quasiregularity in mathematics , see the disambiguation page quasiregular . In mathematics , quasiregular representation is a concept of representation theory , for a locally compact group G and a homogeneous space G H where H is a closed subgroup . In line with the concepts of regular representation and induced representation , G acts on functions on G H . If however Haar measure s give rise only to a quasi invariant measure on G H , certain correction factors have to be made to the action on functions, for L sup 2 sup G H to afford a unitary representation of G on square integrable function s. With appropriate scaling factors, therefore, introduced into the action of G , this is the quasiregular representation or modified induced representation. DEFAULTSORT Quasiregular Representation Category Unitary representation theory Category Topological groups ...   more details



  1. Dual representation

    In mathematics , if G is a group mathematics group and &rho is a linear representation of it on the vector space V , then the dual representation Overline &rho is defined over the dual vector space Overline V as follows ref Lecture 1 of Fulton Harris ref Overline &rho g is the transpose of a linear map transpose of &rho g sup &minus 1 sup for all g in G . Then Overline &rho is also a representation, as may be checked explicitly. The dual representation is also known as the contragredient representation . If math mathfrak g math is a Lie algebra and &rho is a representation of it over the vector space V , then the dual representation Overline &rho is defined over the dual vector space Overline V as follows ref Lecture 8 of Fulton Harris ref Overline &rho u is the transpose of &minus &rho u for all u in math mathfrak g math . Overline &rho is also a representation, as you may check explicitly. For a unitary representation , the conjugate representation and the dual representation coincide, up to equivalence of representations. Generalization A general ring Module mathematics module does not admit a dual representation. Modules of Hopf algebra s do, however. See also Complex conjugate representation Kirillov Character Formula References references Category Representation theory of groups ...   more details




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