The Matrixcode 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
, the code that comprises the Matrix itself is frequently represented as downward flowing ...About the 1999 film the franchise it initiated The Matrix franchise other uses Infobox film name The Matrix image The Matrix Poster.jpg caption Theatrical release poster director ubl The Wachowskis Andy ... name boxoffice The Matrix is a 1999 American science fiction film science fiction action film written ... sequels, and the The Matrix franchise Matrix franchise was further expanded through the production ... source. Upon learning this, computer programmer Neo The Matrix Neo is drawn into a rebellion against ... detail to this summary. Computer programmer Neo The Matrix Thomas Anderson Keanu Reeves is secretly ... references to the Matrix appearing on his computer. A female hacker named Trinity The Matrix Trinity Carrie Anne Moss confirms that a man named Morpheus The Matrix Morpheus Laurence Fishburne can help him however, three sinister Agent The Matrix Agents , led by Agent Smith Hugo Weaving , arrest ... energy of humans, who are kept docile within the Matrix, a simulated reality of the world as it was in 1999. Morpheus and his crew belong to a group of free humans who unplug others from the Matrix ... within the Matrix by using their understanding of its true nature to manipulate its physical law s. Neo is warned that fatal injuries within the Matrix will also kill one s physical body, and that the Agents ... the Matrix to visit the Oracle The Matrix Oracle Gloria Foster , who predicted the emergence of the One ... escape. Their ally Cypher The Matrix Cypher Joe Pantoliano had betrayed them, making a deal for a permanent return to the comfortable life of the Matrix in exchange for giving Morpheus to the Agents. Cypher murders three crew members before he is killed by Tank The Matrix Tank Marcus Chong . The Agents ... in Zion The Matrix Zion , the humans subterranean refuge in the real world. Neo and Trinity return to the Matrix and rescue their leader in the process, Neo becomes more confident in his ability to manipulate ... more details
wiktionary Matrix may refer to TOCright Math and science Matrix mathematics , a rectangular array of numbers, symbols or expressions Matrix biology , the material or tissue between cells in which more specialized structures are embedded Matrix chemical analysis , the non analyte components of a sample Matrix geology , the fine grained material in which larger objects are embedded Harris matrix , an archeological tool Metal matrix , material used in a metal matrix composite Matrix isolation , an experimental technique in chemistry and physics Film and television The Matrix franchise The Matrix franchise , a science fiction franchise The Matrix , the first film in the franchise The Matrix Music from the Motion Picture , a soundtrack album Matrix TV series Matrix TV series Matrix Doctor Who Matrix Doctor Who , a computer system Matrix, a ReBoot character John Matrix, a Commando film Commando character Music and audio Matrix music , an unchanging element of variations Matrix artist , a British DJ Matrix jazz group The Matrix production team M rix , an album by P.A.L. Clave matrix Keyboard matrix circuit Matrix decoder , a technology for converting audio channels Matrix or matrix master , a master disc used in the production of gramophone records Matrix , a song by Chick Corea on the album Now He Sings, Now He Sobs Comics and literature Matrix comics , a DC Comics character Matrix Doctor Who novel Matrix Doctor Who novel , by Robert Perry and Mike Tucker Matrix of Leadership , a Transformers plot element Matrix, a Neuromancer plot element Business and law MATRIX Northern Ireland Science Industry Panel Matrix Business Technologies , a telecommunications firm Matrix Chambers , a barristers set Matrix Games , an American video game publisher founded 1999 Matrix management , an organizational management style Matrix Partners , a private equity investment firm Matrix Software , a Japanese video game developer founded 1994 Growth share matrix , a business analysis technique Transportation ... more details
The code may refer to The Code band , a ska punk band The Code 2001 film , a 2001 documentary about Linux Thick as Thieves 2009 film , a 2009 film also known as The Code The Code TV series , a 2007 Australian police documentary The Code UK TV series , a 2011 British mathematics documentary An unwritten set of rules, for example in Fighting in ice hockey Etiquette ice hockey The Motion Picture Production Code aka Hays Code , a set of movie industry guidelines for censorship widely used between 1930 1968 See also Code disambiguation disambig it The Code ... more details
Category Walsh matrix Walsh matrix Haar wavelet Quincunx matrix Hadamard transform Code division multiple access Notes reflist DEFAULTSORT Walsh Matrix Category Matrices it Matrice di Walsh sl Walshova ...File Walsh 16 Gould s Morse.svg thumb 320px Walsh matrix of order 16 multiplied with a vector File Natural and sequency ordered Walsh 16.svg thumb 320px Natural ordered Hadamard matrix permuted into sequency ordered Hadamard matrix br br The number of sign changes per row in the natural ordered matrix is br 0,15, 7,8, 3,12, 4,11, 1,14, 6,9, 2,13, 5,10 , br in the sequency ordered matrix the number of sign changes is consecutive ... matrix br The ones in the triangular matrices form Sierpinski triangle Sierpinski triangles . The entries of the diagonal matrix are values from oeis A001316 Gould s sequence , with the minus signs distributed like the ones in Thue Morse sequence . File Binary Walsh matrix 16.svg thumb 320px Binary Walsh matrix as a w Matrix multiplication matrix product br The binary matrix white 0, red 1 is the result ... in Real number R . 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 .... 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 Recursion recursive formula below, and the sequency ordered Hadamard matrix is formed ... to either matrix as the Walsh matrix. The Walsh matrix and Walsh function s are used in computing ... by the recursive formula The lowest order of Hadamard matrix is 2 math H 2 1 begin bmatrix ... matrix can be derived from the ordering of the Hadamard matrix by first applying the bit reversal permutation and then the Gray code permutation . ref cite journal last Yuen first C. year 1972 ... more details
code in exchange for their daughter s passage into the Matrix as an Exile via the Trainman. In reality ...DISPLAYTITLE Oracle The Matrix Infobox character colour green colour text lightgreen name The Oracle series The Matrix franchise The Matrix image Image The Oracle i .gif caption Gloria Foster as the Oracle. first The Matrix last The Matrix Revolutions cause creator The Wachowskis Wachowski Brothers portrayer Gloria Foster The Matrix and The Matrix Reloaded br Mary Alice The Matrix Revolutions episode ... nationality The Oracle is a fictional character in The Matrix franchise The Matrix franchise . She ... films and Mary Alice in the third film. The character also appears in the video game Enter the Matrix and the MMORPG The Matrix Online . Overview In the first film, she is a mysterious but powerful figure ... Matrix fictional universe the Matrix s system. Later, she is revealed to be a Sapience sapient computer program program who is integral to the very nature of the Matrix itself. Whether her power ... power cannot be used to predict the ultimate consequences of Neo The Matrix Neo , who possesses free will when he defies the Architect The Matrix Architect . Her power of foresight, on the other ... thus, allowing the Matrix to become more accustomed for the majority of the human population to accept. She exhibits a trait for predicting events directly relevant to the nature and or programming of the Matrix ... is her prediction about Neo s choice in the second movie, The Matrix Reloaded she had existed ... .jpg thumb left Mary Alice as the Oracle. The Oracle is played by Gloria Foster in The Matrix and The Matrix Reloaded , and by Mary Alice in The Matrix Revolutions and Enter the Matrix , one of the franchise s video games. In The Matrix Revolutions and Enter the Matrix , it is explained that Kamala ... role in Matrix Revolutions was shot. In the third Matrix movie, the Oracle hints at her true purpose, which is to bring imbalance, rather than balance, to the equations that form the Matrix. In that she ... more details
CODE may refer to Crude Oil Data Exchange , an electronic business standard sanctioned by the American Petroleum Institute Cultural Olympiad Digital Edition CODE programming language Confederaci n de la Democracia 1972 , a defunct political coalition in Chile Code disambiguation disambig ... more details
In coding theory , a generator matrix is a Basis linear algebra basis for a linear code , generating all its possible codewords. If the matrix is G and the linear code is C , w c G where w is a codeword of the linear code C , c is a row vector, and a bijection exists between w and c . A generator matrix for an math n math , math M q k math , math d math sub math q math sub code has dimensions k n . Here n is the length of a codeword, k is the number of information bits, d is the minimum distance of the code, and q is the number of symbols in the alphabet thus, q 2 indicates a binary code , etc. . The number of Redundancy information theory redundant bits is denoted by r n k . The Systematic code systematic form for a generator matrix is math G begin bmatrix I k P end bmatrix math where math I k math is a k k identity matrix and P is of dimension k r . A generator matrix can be used to construct the parity check matrix for a code and vice versa . Equivalent Codes Codes C sub 1 sub and C sub 2 sub are equivalent denoted C sub 1 sub C sub 2 sub if one code can be created from the other via the following two transformations ol li permute components, and li scale components. ol Equivalent codes have the same distance. The generator matrices of equivalent codes can be obtained from one another via the following transformations ol li permute rows li scale rows li add rows li permute columns, and li scale columns. ol See also Hamming code 7,4 External links http mathworld.wolfram.com GeneratorMatrix.html MathWorld entry DEFAULTSORT Generator Matrix Category Coding theory cs Generuj c matice de Generatormatrix fr Matrice g n ratrice ja sl Generatorska matrika ... more details
Multiple issues wikify March 2012 orphan March 2012 notability January 2009 Each function in SAP ERP has an SAP Transaction Code associated with it. A transaction code or t code consists of letters, numbers, or both. You enter transaction codes in the command field. Use A transaction code will take you to any task in an SAP application faster. By entering a transaction code instead of using the menu, you navigate to a task and start the function in a single step. Like for creating users in SAP SU01 and for maintenance T code SU10 . T Codes are like shortcuts in windows OS. External links http tcodes.ofsap.com All SAP Transaction Codes details categorized by modules with SAP menu path http www.saptrainingtutorial.com SAP Tutorials Tcodes SAP Transaction Codes uses with respective module http www.saptutorials.com SAP Transaction Codes Largest SAP transaction codes repository on the web with easy navigation and description in four languages English, German, French and Dutch http www.easymarketplace.de transactions.php T Code look up SAP Transaction Codes with Report and Description http www.smart words.org sap transaction codes overview.html SAP Transaction Codes Overview The most useful SAP Transaction Codes incl. pdf for download Category SAP AG Category ERP software ... more details
matrix . Coordinate list COO COO stores a list of code row, column, value code tuples. Ideally, the entries ... code i code . Row code i code of the original matrix extends from code A IA i code to code A IA i 1 ... code . For example, the matrix 1 2 0 0 0 3 9 0 0 1 4 0 is a three by four matrix with six nonzero elements ... values of the matrixcode col ind code is the column indices corresponding to the values and, code ... bottom non zero values of the matrixcode row ind code is the row indices corresponding to the values ... a sparse matrix in MATLAB via the code sparse code function . Example A bitmap image having ... Ragged matrix Skyline matrix Sparse array Sparse graph code Sparse file Harwell Boeing file format ...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 ... 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 .... Storing a sparse matrix The native 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 Array data structure indices i and j . For an m n matrix, enough memory to store up to m n entries to represent the matrix is needed. Substantial memory requirement reductions can be realized by storing ..., 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 operations. Dictionary of keys DOK DOK represents non zero values as a dictionary mapping code row, column ... more details
Infobox anatomy Name Nail matrix Latin matrix unguis GraySubject GrayPage Image Caption Image2 Caption2 Map MapPos MapCaption Precursor System Artery Vein Nerve Lymph MeshName MeshNumber Code Terminologia Histologica TH H3.12.00.3.02020 The nail matrix is the formative layer of Cell biology cells at the base of the Nail anatomy fingernail or toenail. This tissue consists of rapidly dividing skin cells that soon fill with the protein keratin . The matrix of finger nails consists of the most rapidly dividing skin cells in the body, which grow four times faster than toenails at a rate of approximately 3mm a month. See also Runner s toe , repetitive injury seen in runners External links http medical dictionary.thefreedictionary.com nail bed http medical dictionary.thefreedictionary.com matrix Integumentary system Category Nail anatomy Anatomy stub de Nagelmatrix ... more details
of a floating figure made of golden code when within The Matrix. Initially emotionally distraught ...DISPLAYTITLE Trinity The Matrix Refimprove date July 2009 Infobox character colour black colour text white name Trinity series The Matrix franchise The Matrix image caption first The Matrix last The Matrix ... Hale voice in The Matrix Path of Neo episode nickname Trin alias species Human gender Female occupation title First Mate of the List of ships in the Matrix series Nebuchadnezzar .28.22Neb.22.29 Nebuchadnezzar ... s Romantic interest love interest in The Matrix franchise The Matrix franchise . She is portrayed ... Moss as Trinity in The Matrix Reloaded Trinity first appears in the original Matrix film and she becomes ... the Matrix, a sophisticated computer program in which most of the human race is imprisoned. Though few specifics are revealed about her previous life inside the Matrix, we are told that she cracked a database so secure that she is famous amongst hackers, and that Morpheus The Matrix Morpheus , one ... the program. At the beginning of the series, she is first mate on Morpheus List of ships in the Matrix ... he wishes to free from the Matrix. As the series progresses, her primary importance as a character becomes her close relationship with Neo The Matrix Neo . She is skilled with computers, at operating vehicles both inside and outside the Matrix, and in martial arts. Throughout the series, her Matrix given name is never revealed. Role in the films The Matrix Trinity is first introduced at the beginning of The Matrix , in a phone conversation with List of minor characters in the Matrix series Cypher ... and a group of police officers. Also on hand are Agent The Matrix Agents , sentient programs that police the Matrix to pinpoint potential troublemakers and neutralize them. Trinity is next seen communicating ... s crew unplug Neo from the Matrix and begin his training as a new recruit in the war against the machines. She participates in several missions into the Matrix, including taking Neo to Oracle The Matrix ... more details
and return the critical Source code he carried for the eventual reloading of the Matrix. A New Matrix Together with the human intuitive program which could be considered the mother of the Matrix ... that would fulfill these prophecies. The One was made carrying not only the source code of the Matrix ... the Matrix source code would be reinserted into the program, allowing for the system to reboot. Zion ...For other uses of the term Architect disambiguation DISPLAYTITLE Architect The Matrix In universe date ... The Architect series The Matrix franchise The Matrix image Image TheArchitectMatrix.jpg 300px caption first The Matrix Reloaded last cause creator The Wachowskis Wachowski Brothers portrayer Helmut ... title Creator of the Matrix fictional universe the Matrix callsign family spouse children relatives residence religion nationality The Architect is a fictional character in the last two films of the The Matrix franchise Matrix trilogy , created by the The Wachowskis Wachowski brothers . The character is played by Helmut Bakaitis . He also makes an appearance in the MMORPG The Matrix Online . History Constructing the First Matrices The Architect created the first Matrix as a utopia for the humans ... 1 of the Matrix crashed. A second attempt added vulgarities of human nature and a basic cause ... to understand human nature and psychology to augment the framework of the next Matrix. This time ..., even if the person was only aware of the choice on a vague, unconscious level. This version of the Matrix ... that the Matrix was not as perfect as he would have wanted. The choice programming that stabilized the first iteration of the Matrix was also causing its destabilization. In approximately 100 years time, a reload of the Matrix would be required. There was also the matter of Zion, which could not be allowed ... to the Machine City. One significant anomaly appeared two thirds into the Matrix first cycle. A man was born with control of additional Matrix programming that actually belonged with the Source. The Architect ... more details
and the associated patient status designation Do not resuscitate Infobox album Name No Code Type studio ... Brendan O Brien music producer Brendan O Brien , Pearl Jam Last album Vitalogy br 1994 This album No Code br 1996 Next album Yield album Yield br 1998 Misc Singles Name No Code Type studio single 1 Who ... single 3 Off He Goes single 3 date 1996 No Code is the fourth studio album by the American alternative ... rock , worldbeat , psychedelia , and experimental music experimentalism . Although No Code debuted ... album, Pearl Jam again worked with producer Brendan O Brien music producer Brendan O Brien . No Code ... of Vitalogy . Following the summer U.S. leg of the band s Vitalogy Tour , the band began work on No Code ... , Georgia U.S. state Georgia . ref 1996 Album notes for No Code by Pearl Jam, CD booklet . New ... that the band was more on the fly during the making of No Code , and some good thing happened out ... finishes off the songs...But by the end of No Code , he was so burnt, it was so much work for him ... Vedder said, Making No Code was all about gaining perspective. ref name spin Marks, Craig. The Road ... production, No Code represented a deliberate break from Ten Pearl Jam album Ten s anthemic ... name spin David Browne of Entertainment Weekly stated that No Code displays a wider range of moods ... is given credit in the No Code Gramophone record vinyl , but the credit is inexplicably absent from ... USA TODAY pre 1997 Fulltext &desc Grunge gurus break Code Pearl Jam s exotic jumble&pqatl google Review No Code . USA Today 01.D. August 23, 1996. ref rev2 Pitchfork Media rev2Score 5.4 10 ref name ... reviews p pearl jam no code.shtml Pearl Jam No Code . Pitchfork Media . September 1, 1996. Retrieved on May 20, 2009. ref rev3 NME rev3Score 7 10 ref name nme August 24, 1996 . Review No Code . NME p. 50 . ref rev4 Q magazine Q rev4Score Rating 4 5 ref name q October 1996 . Review No Code . Q magazine ... 08 25 ref rev6 Allmusic rev6Score Rating 3.5 5 ref name allmusic cite web title allmusic No Code Review ... more details
. These attacks take the form of weapons that reveal the Matrix s inner workings its code for all human ... his leaving, the Assassin bends the code of the Matrix and emerges from a vent in the wall. Morpheus ... Morpheus series The Matrix franchise The Matrix image caption first The Matrix last cause creator The Wachowskis ... Male occupation title Captain of the List of ships in the Matrix series Nebuchadnezzar .28.22Neb.22.29 ... protagonist of The Matrix franchise The Matrix franchise . The The Wachowskis Wachowski brothers co writers and directors of The Matrix films were fans of Neil Gaiman and based the character of Morpheus ... needed date March 2012 Morpheus voice role in The Matrix Path of Neo is retained by Laurence .... 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 Zion , in a devastated world where most humans are grown by sentient machines and kept imprisoned in the Matrix, a virtual computer generated world. Morpheus was once a human living inside the Matrix until he was freed. Morpheus is apparently a very popular public figure in the city of Zion. He 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. The name Morpheus is that of the Morpheus ... s involvement with the dreaming of the Matrix. The mythical Morpheus and his family, including two brothers ... to Morpheus in The Matrix, who offers Neo either a blue pill to forget about The Matrix and continue ... Earlier in his life, Morpheus gained the romantic attention of Niobe The Matrix Niobe , another hovercraft captain. Their relationship became estranged shortly after Morpheus visited Oracle The Matrix ... more details
the description and source code of simple sparse matrix routines, still useful even if long superseded. ref is about same as for Cholesky for banded matrices available for banded matrix banded matrices , e.g. in LAPACK for a prototype skyline code, see ref name George . Before storing a matrix in skyline ...A skyline matrix is a form of a square, banded and typically symmetric matrix that reduces the storage requirement of a matrix due to it s banded nature. br br For symmetrical matrices with zero based indexing math A skyline i,j begin cases A original i,j i & mbox if i le j le i bandwidth 0 & otherwise end cases math br For unsymmetrical matrices with zero based indexing math A skyline i,j begin cases ... Examples For a symmetric 6 by 6 matrix A with a bandwidth of 3 turns into the 6 by 3 matrix A skyline . br Matrix A in original format br math begin bmatrix A 11 & A 12 & A 13 & 0 & cdots & 0 & A 22 & A 23 ... & & & & & A 66 end bmatrix math br br Matrix A skyline in skyline format br math begin bmatrix ... & 0 end bmatrix math br br br br For an unsymmetrical 6 by 6 matrix B with left and right band widths of 2 turns into the 6 by 3 matrix B skyline . br Matrix B in original format br math begin bmatrix ... 0 & cdots & cdots & 0 & B 65 & B 66 end bmatrix math br br Matrix B skyline in skyline format br math ... 55 & B 56 B 65 & B 66 & 0 end bmatrix math Skyline Matrix storage skyline matrix storage , or SKS, or a variable band matrix storage , or envelope storage scheme ref Citation title Fundamentals of matrix ...&f false ref is a form of a sparse matrix storage format matrix that reduces the storage requirement of a matrix more than band matrix banded storage . In banded storage, all entries within a fixed ... systems of linear equations with a symmetric, positive definite matrix all Sparse matrix Reducing ... 19 853408 6 ref which store only the nonzero entries of the matrix, become more efficient for very large problems due to much less fill in. See also Sparse matrix Banded matrix Frontal solver References ... 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
. It is then shown that he is able to perceive, interpret, and alter the computer code of the Matrix ... the rest of the Matrixcode by shattering him, giving him a life independent of the machine s systems ... bartered. Neo then dies, his primary code being inserted into the Matrix which allows it to reboot ..., since his inception, the Matrix s source code known as the Prime Program. This gives him the ability ...DISPLAYTITLE Neo The Matrix Multiple issues original research June 2008 in universe October 2009 refimprove ... caption Neo in The Matrix Reloaded name Thomas Anderson Neo series The Matrix franchise The Matrix first The Matrix last cause creator The Wachowskis Wachowski Brothers portrayer Keanu Reeves films voice Andrew Bowen The Matrix Path of Neo episode nickname The Anomaly name for him given by the machines br Mr. Anderson Agent Smith calls him by his Matrix name alias Neo species Human gender Male birthdate September 11, 1962 occupation Hacker br The One warrior br Former software engineer in the Matrix .... Anderson is a fictional character and the main protagonist of The Matrix franchise The Matrix ... by Keanu Reeves in The Matrix Trilogy and The Animatrix . Andrew Bowen provided Neo s voice in The Matrix ... a respected member of the school community through his involvement in football and hockey. The Matrix ... to the Matrix, unaware that the world he lives in is a virtual reality. ref This name carries several ... the truth of the risen Christ. In The Matrix, Thomas Anderson sheds his disbelief and comes to accept that the Matrix is real and he is thereby born again, and is referred to as Neo. He also comes ... has learned about something known only as Matrix fictional universe The Matrix . It is described ... . During the years prior to the events of The Matrix , Anderson has spent his time trying to find the one man who he thought could tell him what the Matrix was a supposed terrorist known only as Morpheus. Anderson is suddenly contacted by Morpheus The Matrix Morpheus via a cell phone mailed ... more details
dablink A related concept is that of a triangular array . for the rings triangular matrix ring File Cyclic group Z4 Cayley table powers of Gray code permutation small .svg thumb Logical matrix Binary lower unitriangular Toeplitz matrix Toeplitz matrices, multiplied using Finite field F sub 2 sub operations br They form the Cayley table of cyclic group Z sub 4 sub and correspond to v Gray code permutation powers 4 bit powers of the 4 bit Gray code permutation . In the mathematics mathematical discipline of linear algebra , a triangular matrix is a special kind of square matrix square matrix mathematics matrix . A square matrix is called lower triangular if all the entries above the main diagonal are zero. Conversely a square matrix is called upper triangular if all the entries below the main diagonal are zero. A triangular matrix is one that is either lower triangular or upper triangular. A matrix that is both upper and lower triangular is a diagonal matrix . Because matrix equations with triangular ... decomposition algorithm, any invertible matrix may be written as the product of a lower triangular matrix L by an upper triangular matrix U . Description A matrix of the form math L begin bmatrix l 1,1 ... n,2 & ldots & l n,n 1 & l n,n end bmatrix math is called a lower triangular matrix or left triangular matrix , and analogously a matrix of the form math U begin bmatrix u 1,1 & u 1,2 & u 1,3 & ldots ... n,n end bmatrix math is called an upper triangular matrix or right triangular matrix . The variable L standing for lower or left is commonly used to represent a lower triangular matrix, while the variable U standing for upper or R standing for right is commonly used for upper triangular matrix. A matrix that is both upper and lower triangular is diagonal matrix diagonal . Matrices that are similar matrix similar to triangular matrices are called triangularisable . The standard operations on triangular ... upper triangular matrix is upper triangular. The product of an upper triangular matrix by a constant ... more details
An MDS matrix Maximum Distance Separable is a matrix mathematics matrix representing a function with certain diffusion cryptography diffusion properties that have useful applications in cryptography . Technically, an m× n matrix A over a finite field K is an MDS matrix if it is the transformation matrix of a linear transformation f x Ax from K sup n sup to K sup m sup such that no two different m n tuples of the form x,f x coincide in n or more components. Equivalently, the set of all m n tuples x,f x is an Maximum distance separable code MDS code , i.e. a linear code that reaches the Singleton bound . Let math tilde A left begin array c rm Id n hline rm A end array right math be the matrix obtained by joining the identity matrix Id sub n sub to A. Then a necessary and sufficient condition for a matrix A to be MDS is that every possible n× n submatrix obtained by removing m rows from math tilde A math is non singular matrix non singular . Reed Solomon code s have the MDS property and are frequently used to obtain the MDS matrices used in cryptographic algorithms. Serge Vaudenay suggested using MDS matrices in cryptographic primitive s to produce what he called multipermutations , not necessarily linear functions with this same property. These functions have what he called perfect diffusion changing t of the inputs changes at least m t 1 of the outputs. He showed how to exploit imperfect diffusion to cryptanalysis cryptanalyze functions that are not multipermutations. MDS matrices are used for diffusion in such block cipher s as Advanced Encryption Standard AES , SHARK , Square cipher Square , Twofish , Manta cipher Manta , Hierocrypt , and Camellia cipher Camellia , and in the stream cipher MUGI and the cryptographic hash function WHIRLPOOL . References cite conference author Serge Vaudenay title On the Need for Multipermutations Cryptanalysis of MD4 and SAFER conference 2nd International Workshop on Fast Software Encryption FSE 94 pages 286&ndash 297 publisher ... more details
, because there are 20 amino acids coded for by the genetic code . Therefore, the similarity matrix for amino acids contains 400 entries although it is usually symmetric matrix symmetric . The first ...Distinguish similar matrix A similarity matrix is a matrix mathematics matrix of scores which express the similarity between two data points. Similarity matrices are strongly related to their counterparts, distance matrix distance matrices and substitution matrix substitution matrices . Use in sequence alignment Similarity matrices are used in sequence alignment . Higher scores are given to more similar characters, and lower or negative scores for dissimilar characters. Nucleotide similarity matrices are used to align nucleic acid sequences. Because there are only four nucleotides commonly found in DNA Adenine A , Cytosine C , Guanine G and Thymine T , nucleotide similarity matrices are much simpler than protein similarity matrices. For example, a simple matrix will assign identical bases a score of 1 and non identical bases a score of 1. A more complicated matrix would give a higher score to transitions changes from a pyrimidine such as C or T to another pyrimidine, or from a purine such as A or G to another purine than to transversions from a pyrimidine to a purine or vice versa . The match mismatch ratio of the matrix sets the target evolutionary distance. ref cite journal journal Methods a companion to methods in enzymology volume 3 issue 1 pages 66 year 1991 author States, D ... Nature Biotechnology title Where did the BLOSUM62 alignment score matrix come from? author Sean ... matrix used by BLASTN is best suited for finding matches between sequences that are 99 identical a 1 1 or 4 4 matrix is much more suited to sequences with about 70 similarity. Matrices for lower similarity ... based on how many base changes were required to change a codon to code for that amino acid ... references DEFAULTSORT Similarity Matrix Category Bioinformatics Category DNA Category Matrices ... 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. Sansui QS Regular Matrix system for Quadraphonic sound. mathdab ... more details
minimum distance math 2 n 1 math with Linear code Popular notation generating matrix math F n ...In mathematics , an Hadamard matrix , named after the French mathematician Jacques Hadamard , is a square matrix whose entries are either 1 or &minus 1 and whose rows are mutually orthogonal . In geometric terms, this means that every two different rows in a Hadamard matrix represent two perpendicular ... matrix has the maximum possible n dimensional volume among parallelotopes spanned by vectors whose entries are bounded in absolute value by 1. Equivalently, a Hadamard matrix has maximal determinant ... as an error correcting code using a Hadamard code generalized in Reed Muller code s , and are also ... estimator . Properties It follows from the definition that a Hadamard matrix H of order n satisfies math H H mathrm T n I n math where I sub n sub is the n × n identity matrix and H sup ... is a complex matrix of order n , whose entries are bounded by M sub ij sub 1, for each i , j between ... det M leq n n 2 . math Equality in this bound is attained for a real matrix M if and only if M is a Hadamard matrix. The order of a Hadamard matrix must be 1, 2, or a multiple of 4. Sylvester s construction .... Let H be a Hadamard matrix of order n . Then the partitioned matrix math begin bmatrix H & H H & H end bmatrix math is a Hadamard matrix of order 2 n . This observation can be applied repeatedly and leads to the following sequence of matrices, also called Walsh matrix Walsh matrices . math H 1 begin ... of special properties. They are Symmetric matrix symmetric and have Trace linear algebra trace ... map the elements of the Hadamard matrix using the group homomorphism math 1, 1, times mapsto 0,1, oplus math , we can describe an alternative construction of Sylvester s Hadamard matrix. First consider the matrix math F n math , the math n times 2 n math matrix whose columns consist of all n bit ... n 1 end bmatrix . math It can be shown by induction that the image of the Hadamard matrix under the above ... 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
within the Matrixcode against scans. Zion used this new found ability to track down and re capture ...Infobox character colour white colour text black name Seraph series The Matrix franchise The Matrix image caption first The Matrix Reloaded last cause creator The Wachowskis Wachowski Brothers portrayer ... title Guardian of the Oracle The Matrix Oracle callsign family spouse children relatives residence ... 2006 Seraph is the name of a fictional character in the films The Matrix Reloaded and The Matrix Revolutions ... protocol which guards the Oracle Matrix character Oracle . He is portrayed by Collin Chou . The role ... could do well without his presence, Chou signed on. The Matrix Trilogy In The Matrix Reloaded and The Matrix Revolutions , Seraph is seen acting as a guardian angel of the Oracle. He refers ... with warriors of Zion The Matrix Zion . The first is with Ballard, which he stages in order to get to know him the second, with Neo Matrix character Neo , to prove he is the One . The third takes place in the closing stages of Enter the Matrix , after the conclusion of Reloaded but before the beginning of Revolutions . Seraph summons either Niobe The Matrix Niobe or her First Mate List of minor characters in the Matrix series Ghost Ghost to meet the Oracle. Whoever he summons, he first tests ..., a Challenge response authentication . In Revolutions , Trinity The Matrix Trinity and Morpheus The Matrix ... within a place that is neither the Matrix fictional universe Matrix nor the Machine world a construct ... is uncertain. In The Matrix Online he claims he isn t allied with any of the three Factions, that he ..., it was revealed that Seraph had been an Agent of the first iteration of the Matrix the Seraphim ... even by any one in the Matrix, considering he was originally an Agent himself, along with the super ... entity in Matrix whom he could not defeat in a one on one confrontation. Despite not having his wings ... pills, absorbing, altering, or deleting something within their code. This has recently been revealed ... more details
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