In the field of artificial intelligence , a confusion matrix is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one in unsupervised learning it is usually called a matching matrix . Each column of the matrix represents the instances in a predicted class, while each row represents the instances in an actual class. The name stems from the fact that it makes it easy to see if the system is confusing two classes i.e. commonly mislabeling one as another . Outside artificial intelligence , the confusion matrix is often called the contingency table or the error matrix. ref cite journal last1 Stehman first1 Stephen V. year 1997 title Selecting and interpreting measures of thematic classification accuracy journal Remote Sensing of Environment volume 62 issue 1 pages 77 89 doi 10.1016 S0034 4257 97 00083 7 ref Example If a classification system has been trained to distinguish between cats, dogs and rabbits, a confusion matrix will summarize the results of testing the algorithm for further inspection. Assuming a sample of 27 animals &mdash 8 cats, 6 dogs, and 13 rabbits, the resulting confusion matrix could look like the table ... In this confusion matrix, of the 8 actual cats, the system predicted that three were dogs, and of the six dogs, it predicted that one was a rabbit and two were cats. We can see from the matrix that the system ... of confusion sometimes also called a confusion matrix as if the name wasn t confusing enough , is a table ..., because it will yield misleading results if the data set is unbalanced that is, when the number of samples in different classes vary greatly . For example, if there were 95 cats and only 5 dogs in the data ... class but a 0 recognition rate for the dog class. Assuming the confusion matrix above, its corresponding ... dbd cs831 notes confusion matrix confusion matrix.html Theory about the confusion matrix http www.gabormelli.com RKB Confusion Matrix GM RKB Confusion Matrix concept page Category Machine learning ... more details
Refimprove date December 2009 In the mathematics mathematical discipline of matrix theory , a block matrix or a partitioned matrix is a matrix mathematics matrix broken into sections called blocks . Looking at it another way, the matrix is written in terms of smaller matrices. ref name MITlecture http ... the matrix is split into blocks by horizontal and vertical lines, which must cut the matrix completely in the given direction. The block matrix may also have an block matrix pseudoinverse inverse . Example File BlockMatrix168square.png thumb A 168 168 element block matrix with 12 12, 12 24, and 24 24 sub Matrices. Non zero elements are in blue, zero elements are grayed. The matrix math mathbf ... begin bmatrix 4 & 4 4 & 4 end bmatrix . math The partitioned matrix can then be written as math mathbf P begin bmatrix mathbf P 11 & mathbf P 12 mathbf P 21 & mathbf P 22 end bmatrix . math Block matrix multiplication A block partitioned matrix product can be formed involving operations only on the submatrices. Given an math m times p math matrix math mathbf A math with math q math row partitions ... & mathbf A q2 & cdots & mathbf A qs end bmatrix math and a math p times n math matrix math mathbf B ... & vdots & ddots & vdots mathbf B s1 & mathbf B s2 & cdots & mathbf B sr end bmatrix , math the matrix ... as an math m times n math matrix with math q math row partitions and math r math column partitions. The matrices in your matrix math mathbf C math are calculated by multiplying while you multiply math ... anchor Block diagonal matrix A block diagonal matrix is a block matrix which is a square matrix .... A block diagonal matrix A has the form math mathbf A begin bmatrix mathbf A 1 & 0 & cdots & 0 ... where A sub k sub is a square matrix in other words, it is the Direct sum of matrices direct sum ... matrix . Any square matrix can trivially be considered a block diagonal matrix with only one .... math The inverse of a block diagonal matrix is another block diagonal matrix, composed of the inverse ... more details
John Moores University H, N 13578 data for universities are for 2002 from 7 At math alpha 1 math the matrix ... thumb 240px Fig.1. Google matrix of Wikipedia articles network, written in the bases of PageRank index fragment of top 200 X 200 matrix elements is shown, total size N 3282257 from 19 A Google matrix is a particular stochastic matrix that is used by Google s PageRank algorithm. The matrix represents a graph with edges representing links between pages. The rank of each page can be generated iteratively from the Google matrix using the power method . However, in order for the power method to converge, the matrix must be stochastic, Irreducible mathematics irreducible and aperiodic . H matrix In order to generate the Google matrix, we must first generate a matrix H representing ... j math , and 0 otherwise this is the adjacency matrix of links. Divide each row by math k i math where math k i math is the total number of links to other pages from node i . The matrix H is usually .... G matrix Image Googlematrixcambridge2006.jpg thumb 260px Fig.2. Google matrix of Cambridge University network 2006 , coarse grained matrix elements are written in the bases of PageRank index, total .... We can first generate the stochastic matrix S from H by adding an edge from every sink state math a math to every other node. In the case where there is only one sink state the matrix S is written ... a relation between nodes without a relation with a factor of math alpha math , the matrix will become ... making it aperiodic. The final Google matrix G can be computed as math G alpha S 1 alpha frac 1 N e e T 1 math By the construction the sum of all non negative elements inside each matrix column is equal ... math a math , the Google matrix can be written as math G alpha H alpha a 1 alpha e frac 1 N e T. math Although G is a dense matrix, it is computable using H which is a sparse matrix. Usually for modern directed networks the matrix H has only about ten nonzero elements in a line, thus only about 10 N ... more details
. From it a transformation matrix can be derived that allows one to completely decorrelate the data ... X M 1 2 M. , math How to find a valid covariance matrix In some applications e.g. building data models from only partially observed data one wants to find the nearest covariance matrix to a given symmetric ... density function centered at 0,0 , with covariance matrix 1.00, .50 .50, 1.00 . Image GaussianScatterPCA.png ...× 2 covariance matrix is needed the directions of the arrows correspond to the eigenvectors of this covariance matrix and their lengths to the square roots of the eigenvalues . In probability theory and statistics , a covariance matrix also known as dispersion matrix or variance covariance matrix is a Matrix mathematics matrix whose element in the i , j position is the covariance between the i .... Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions ... of the necessary information a 2× 2 matrix would be necessary to fully characterize the two dimensional variation. Analogous to the fact that it is necessary to build a Hessian matrix to fully describe the concavity of a multivariate function , a covariance matrix is necessary to fully describe ... matrix is the matrix whose i , j entry is the covariance math Sigma ij mathrm cov X i, X j mathrm ... mu 2 & cdots & mathrm E X n mu n X n mu n end bmatrix . math The inverse of this matrix, math Sigma 1 math , is the inverse covariance matrix , also known as the concentration matrix or precision matrix ... matrix have an interpretation in terms of partial correlation s and partial variance s. Citation needed date February 2012 Generalization of the variance The definition above is equivalent to the matrix ... this matrix the variance of the random vector math X math , because it is the natural generalization to higher dimensions of the 1 dimensional variance. Others call it the covariance matrix , because it is the matrix of covariances between the scalar components of the vector math X math . Thus math ... more details
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 title Improved sensitivity of nucleic acid database searches using application specific scoring matrices ... 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 ..., 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 ... 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
In mathematics and multivariate statistics , the centering matrix ref John I. Marden, Analyzing and Modeling Rank Data , Chapman & Hall, 1995, ISBN 0412995212, page 59. ref is a symmetric matrix symmetric and idempotent Matrix mathematics matrix , which when multiplied with a vector has the same effect as subtracting the mean of the components of the vector from every component. Definition The centering matrix of size n is defined as the n by n matrix math C n I n tfrac 1 n mathbb O math where math I n , math is the identity matrix of size n and math mathbb O math is an n by n matrix of all 1 s. This can also be written as math C n I n tfrac 1 n mathbf 1 mathbf 1 top math where math mathbf 1 math is the column vector of n ones and where math top math denotes matrix transpose . For example math C 1 begin bmatrix 0 end bmatrix math , math C 2 left begin array rrr 1 & 0 0 & 1 end array right frac 1 2 left begin array rrr 1 & 1 1 & 1 end array right left begin array rrr frac 1 2 & frac 1 2 frac 1 2 & frac 1 2 end array right math , math C 3 left begin array rrr 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 ..., it is zero and removing it again has no effect. math C n , math is singular matrix singular . The effects .... math C n , math has a kernel matrix nullspace of dimension 1, along the vector math mathbf 1 math . math C n , math is a projection matrix . That is, math C n mathbf v math is a projection of math mathbf .... Application Although multiplication by the centering matrix is not a computationally efficient ... of multiple vectors stored in the rows or columns of a matrix. For an m by n matrix math X , math , the multiplication ... math removes the means from each of the m rows. The centering matrix provides in particular a succinct way to express the scatter matrix , math S X mu mathbf 1 X mu mathbf 1 math of a data sample math X , math , where math mu tfrac 1 n X mathbf 1 math is the sample mean . The centering matrix allows us to express the scatter matrix more compactly as math S X ,C n X ,C n X ,C n ,C n ,X , X ,C n ,X ... more details
Z matrix may mean Z matrix chemistry , a table of the locations of atoms comprising a molecule Z matrix mathematics , a matrix whose off diagonal entries are less than or equal to zero It may also refer to The matrix of Z parameters , a matrix characterizing an electrical network disambig ... more details
In mathematics , a matrix coefficient or matrix element is a function on a group mathematics group of a special form, which depends on a linear representation of the group and additional data. For the case of a finite group, matrix coefficients express the action of the elements of the group in the specified representation via the entries of the corresponding matrix mathematics matrices . Matrix coefficients of representations of Lie group s turned out to be intimately related with the theory of special functions , providing a unifying approach to large parts of this theory. Growth properties of matrix coefficients play key role in the classification of irreducible representations of locally compact group s, in particular, reductive real and p adic groups. The formalism of matrix coefficients leads to a vast generalization of the notion of a modular form . In a different direction, mixing mathematics mixing properties of certain dynamical system s are controlled by the properties of suitable matrix coefficients. Definition A matrix coefficient or matrix element of a linear representation &rho of a group G on a vector space V is a function f sub v ,&eta sub on the group, of the type ... space , then by the Riesz representation theorem , all matrix coefficients have the form f sub ... and w taken from a standard basis , this is actually the function given by the matrix mathematics matrix entry in a fixed place. Applications Finite groups Matrix coefficients of irreducible representations ... Schur orthogonality relations . The character theory character of a representation &rho is a sum of the matrix ... groups and special functions Matrix coefficients of representations of Lie groups were first considered ... are expressible as the matrix coefficients of representation of Lie groups G . ref http eom.springer.de ... polynomials Jacobi orthogonal polynomials and Bessel functions all arise as matrix coefficients ... , views them as matrix coefficients of certain infinite dimensional unitary representations, automorphic ... more details
Multiple issues wikify February 2012 refimprove August 2010 confusing July 2010 The U matrix unified distance matrix is a representation of a self organizing map SOM where the Euclidean distance between the codebook vector of the neighboring neurons is depicted in a gray scale image. It is used to visualize the data in a high dimensional space on a 2 D image. ref A. Ultsch and H.P. Siemon. Kohonen s self organizing feature maps for exploratory data analysis. In Proc. INNC 90, Int. Neural Network Conf., pages 305 308, Dordrecht, Netherlands, 1990. Kluwer. ref Construction procedure Once the SOM is trained using the input data, it is expected that the final map does not have any twists. In such a case the distance between the neighboring neurons gives an approximation of the distance between different parts of the underlying data. When such distances are depicted in a gray scale image, light colors depict the closely spaced nodes and darker colors indicate the more distant nodes. Thus, groups of light colors can be considered as a clusters, and the dark parts as the boundary regions. This way of representation can help us in visualizing the clusters in the high dimensional spaces. Darker regions indicate that the distance between the nodes is large and lighter regions indicate that the codebook vectors are close. The clusters are separated by the dark gaps. This gives the details about the number of clusters in the data without any human intervention, such as in an unsupervised manner. References Reflist Category Neural networks comp sci stub ... more details
In linear algebra , an orthogonal matrix is a Matrix mathematics Square matrices square matrix with real ... vectors . Equivalently, a matrix Q is orthogonal if its transpose is equal to its inverse matrix ... I is the identity matrix . An orthogonal matrix Q is necessarily Square matrix square , Invertible matrix invertible with inverse nowrap 1 Q sup &minus 1 sup Q sup T sup , Unitary matrix unitary nowrap 1 Q sup &minus 1 sup Q , and Normal matrix normal nowrap 1 Q Q QQ . As a linear transformation , an orthogonal matrix preserves the dot product of vectors, and therefore acts as an isometry of Euclidean ... is a special orthogonal matrix . As a linear transformation, every special orthogonal matrix acts as a rotation. The complex number complex analogue of an orthogonal matrix is a unitary matrix . Overview An orthogonal matrix is the real specialization of a unitary matrix , and thus always a normal matrix . Although we consider only real matrices here, the definition can be used for matrices ... bold u right cdot left Q bold v right , math where Q is an orthogonal matrix. To see the inner product ... basis, the squared length of v is v sup T sup v . If a linear transformation, in matrix ... dimension, and these have no orthogonal matrix equivalent. Orthogonal matrices are important for a number ... matrix. Examples Below are a few examples of small orthogonal matrices and possible interpretations ... matrix with 90 generates a reflection about the line 45 line y x and therefore exchanges x and y it is a permutation matrix , with a single 1 in each column and row and otherwise 0 math begin bmatrix 0 & 1 1 & 0 end bmatrix . math The identity is also a permutation matrix. A reflection is its own inverse, which implies that a reflection matrix is symmetric matrix symmetric equal to its transpose as well as orthogonal. The product of two rotation matrices is a rotation matrix, and the product of two reflection matrices is also a rotation matrix. Higher dimensions Regardless of the dimension ... more details
In statistics , a design matrix is a matrix mathematics matrix of explanatory variable s, often denoted by X , that is used in certain statistical models, e.g., the general linear model . ref Everitt,B.S. 2002 Cambridge Dictionary of Statistics , CUP. ISBN 0 521 91099 x ref ref George E. P. Box Box, G.E.P. , Tiao, G.C. 1973 Bayesian Inference in Statistical Analysis , Wiley. ISBN 0 471 57427 7 Section 8.1.1 ref It can contain indicator variable s ones and zeros that indicate group membership in an ANOVA . The design matrix represents the independent variable s in statistical models which describe observed data often called dependent variables in terms of other known variables explanatory variables . The theory relating to such models makes substantial use of matrix manipulations involving the design matrix see for example linear regression . A notable feature of the concept of a design matrix is that it is able to represent a number of different experimental designs and statistical models, e.g., ANOVA , ANCOVA , and linear regression . Definition In a regression model, written in matrix vector form as math y X beta epsilon, math the matrix X is the design matrix. Examples Simple Regression ... data points y sub i sub , x sub i sub , where i 1, 2, , 7. The model simple ... in matrix form as math begin bmatrix y 1 y 2 y 3 y 4 y 5 y 6 y 7 end bmatrix begin bmatrix 1 & x ... math where the first column of ones in the design matrix represents the y intercept term while the second ... multiple regression with covariates math w i math and math x i math . Again suppose that the data ... y i beta 0 beta 1 w i beta 2 x i epsilon i math This model can be written in matrix terms as math ... ANOVA with 3 groups and 7 observations. The given data set has the first three observations belonging ... and is not included in the matrix because its difference from the reference group itself is necessarily zero. See also Hat matrix References references Category Matrices Category Regression analysis Category ... 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 attachment region Matrix metalloproteinase Matrix protein Bioinformatics and sequence evolution PAM matrix Position specific scoring matrix Similarity matrix Substitution matrix Botany and agriculture Matrix Planting Population biology and ecology Matrix population models DEFAULTSORT Matrix Biology Category ... more details
in universe date February 2012 Primary sources article date January 2008 Zion is a fictional city in The Matrix franchise The Matrix films. It is the last human city on the planet Earth after a cataclysmic ... into the newly constructed bio electric towers with their minds placed in the Matrix fictional universe Matrix to keep them docile. Twenty three prisoners were freed by a mysterious Matrix controlling figure referred to as Neo The Matrix The One and led to the unfinished Zion where they worked to complete ..., and to fight inside and outside the Matrix. After the One s death, the humans learned to survive ... time trying to free the Matrix s population from their virtual prison . Geography refimprove date .... It contains many areas where homeless or new arrivals rescued from the Matrix gather to live ... fight the Machines in the real world with EMP weapons, with crews fighting to free the Matrix s captive human population by journeying into the Matrix itself. EMP devices, despite being ... moment by the Architect The Matrix Architect when he wanted to reload the Matrix. Leadership The city ... characters in the Matrix series Lock Commander Jason Lock . The captains of the Zion Hovercraft Fleet also have strict access to key data in the Zion Mainframe, and have political bearing with the population ... characters in the Matrix series Councilor Hamann Councilor Hamann being the only white male on the council ... and manipulator of the Matrix, manipulated the situation so Zion served as a control for the survival ... not, accept the Matrix for what it was to live in the physical world without having to recapture them this reduced dissent within the Matrix s population and prevented an exponentially growing ... system, allowing the humans that realized the Matrix wasn t real statistically, only a fraction ... the Prime Program , a program code required to maintain the Matrix, allowing the Matrix ... brokered the truce with the Machines. See also Simulated reality References reflist Matrix ... more details
In signal processing , a polyphase matrix is a matrix whose elements are linear filter filter mask s. It represents a filter bank as it is used in sub band coder s alias discrete wavelet transform s. ref name strang1997filterbanks cite book first1 Gilbert last1 Strang author1 link Gilbert Strang first2 ... be written as matrix multiplication matrix vector multiplication math begin array rcl P & & begin pmatrix ... d 1 end pmatrix & & P cdot begin pmatrix a 0, mbox e a 0, mbox o end pmatrix end array math This matrix math P math is the polyphase matrix. Of course, a polyphase matrix can have any size, it need ... of sub band coding by the polyphase matrix is more than about write simplification. It allows the adaptation of many results from matrix theory and module theory . The following properties are explained for a math 2 times 2 math matrix, but they scale equally to higher dimensions. Invertibility Perfect reconstruction The case that a polyphase matrix allows reconstruction of a processed signal from the filtered data, is called perfect reconstruction property. Mathematically this is equivalent to invertibility. According to the theorem of inverse matrix invertibility of a matrix over a ring, the polyphase matrix is invertible if and only if the determinant of the polyphase matrix is a Kronecker ... matrix math P math is also the inverse matrix of math P math . The adjoint matrix is the transposed matrix with adjoint filter s. math P begin pmatrix h mbox e & g mbox e h mbox o leftarrow 1 ... 2 cdot x 2 right math For the math 2 times 2 math polyphase matrix the Euclidean operator norm can ... n math matrix where the operator norm can be obtained via z transform and the spectral radius of a matrix ... and minimizing eigenvalue. Lifting scheme The concept of the polyphase matrix allows matrix decomposition . For instance the decomposition into triangular matrix addition matrices leads to the lifting ... 1998 url http cm.bell labs.com who wim papers factor index.html ref However, classical matrix decompositions ... more details
Image Matrix.svg thumb 247px right Specific elements of a matrix are often denoted by a variable with two ... and first column of a matrix A . In mathematics , a matrix plural matrices , or less commonly matrixes is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries . An example of a matrix with six elements is math begin bmatrix 1 & 9 & 13 20 & 5 & 6 end bmatrix . math Matrices of the same size can be matrix addition added or subtracted element by element. The rule for matrix multiplication is more complicated, and two matrices ... in three dimensional space is a linear transformation. If R is a rotation matrix and v is a column vector a matrix with only one column describing the Position vector position of a point in space ... of two matrices is a matrix that represents the function composition composition of two linear ... . If the matrix is Square matrix square , it is possible to deduce some of its properties by computing its determinant . For example, a square matrix has an inverse matrix inverse if and only if its determinant .... Matrix calculus generalizes classical mathematical analysis analytical notions such as derivative ... of efficient algorithms for matrix computations, a subject that is centuries old and is today an expanding area of research. Matrix mathematics Matrix decomposition methods Matrix decomposition ... to the structure of particular matrix structures, e.g. Sparse matrix sparse matrices and diagonal matrix .... Infinite matrices occur in planetary theory and in atomic theory. A simple example is the matrix representing .... Definition A matrix is a rectangle rectangular arrangement of mathematical expressions that can be simply ... of box bracket s. The horizontal and vertical lines in a matrix are called rows and columns , respectively. The numbers in the matrix are called its entries or its elements . To specify the size of a matrix, a matrix with m rows and n columns is called an m by n matrix or m n matrix, while ... more details
January 2011 orphan January 2010 The Laffey Matrix is a fee schedule used by many United States courts for determining the proper hourly rates for professional legal work. wiktionary matrix Overview For many years the United States Attorney s Office has used the Laffey Matrix USAO Laffey Matrix as a basis for determining attorneys fees in litigation claims. This matrix was first introduced by the court ... area. Courts in the United States look to the Laffey Matrix when they award attorneys fees under ... has been a routinely updated United States Attorney s Office Matrix a table which provides ... DOJ continues to use a version of the Laffey Matrix, whereby a legal fee matrix from the Court ... Adjusted Laffey Matrix. See McDowell v. District of Columbia, Civ. A. No. 00 594 RCL , LEXSEE 2001 ... Laffey Matrix. Interfaith Community Organization v. Honeywell International, Inc., 426 F.3d 694 3rd Cir. 2005 . In updating the matrix to account for inflation from 1989 2003, ICO relied on the legal ... of Appeals noted that the District Court reviewed both indices the DOJ Matrix and the Adjusted Laffey Matrix and decided that the Adjusted Laffey Matrix represented a better measure of prevailing ... Attorney s Laffey Matrix with a matrix similar to that put forward by ICO in this case and concluded ... Matrix in Robinson v. Equifax Information Services, LLC, 560 F.3d 235 4th Cir. 2009 , requiring instead ... Federal courts have accepted the same methodology, adjusting the Laffey Matrix upwards based upon the higher ... judge, however, to rely on official data to determine appropriate hourly rates, not on an attorney ... reliable official source for rates that vary by experience levels is the Laffey matrix used in the District ... have rejected the Adjusted Laffey Matrix, particularly for cases in the Washington Baltimore region, and instead continue to rely on the original Laffey Matrix also known as the USAO Laffey Matrix ... s time. Discounted fees are not incorporated into the data unless the contacted attorney routinely ... 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 Harris matrix is a tool used to depict the temporal succession of archaeological context s and thus the sequence of deposition on a dry land archaeological site. The matrix reflects the relative position and stratigraphic contacts of observable stratigraphic units, or contexts. The Matrix was developed ... developed in the UK which allow indepth analysis of complex archaeological data sets, usually ... Brucesmatrix.png thumb Harris matrix of an urban sequence. The law of superposition In a series ... from 1992 2003. Harris matrix in use In constructing a matrix, the latest Archaeological context contexts sit on top of the matrix and the earliest at the bottom with the lines that link them together ... are physical, not all physical relationships are stratigraphic . The matrix thus demonstrates the temporal ... record. Regular daily checking of the record and the compilation of the matrix itself both help .... Loops are sequences in the matrix that produce temporal anomalies so that the earliest context in a sequence ... excavating such sites to compile the matrix as the excavation progresses. Such sites by definition ... is to compile the matrix by hand based on the drawings and the context sheets. This ensures ... do exist which can aid the production of a matrix, though at the moment these tend towards articulating linear sequences rather than multi linear sequences. The Harris matrix is a tool that aids .... Example of the Harris matrix Image Harris section example.jpg Take this hypothetical Archaeological section section as an example of matrix formation. Here there are twelve Archaeological ... by the following Harris matrix The completed matrix Image Harris matrix example.jpg The later a context s formation is, the higher it is in the matrix, and conversely the earlier it is, the lower ..., so even though wall 2 is physically higher than other contexts in section, its position in the matrix ... and floor happened later. also note the matrix splits into two parts below the construction ... more details
Technical date September 2010 moved from talk page In computer vision , the essential matrix is a math 3 times 3 math Matrix mathematics matrix , math mathbf E math , with some additional properties, which ... Camera matrix Normalized camera matrix and normalized image coordinates normalized image ... which defines the essential matrix was published in 1981 by Longuet Higgins, introducing the concept to the computer vision community. Hartley & Zisserman s book reports that an analogous matrix ... of the essential matrix. Use The essential matrix can be seen as a precursor to the fundamental matrix computer vision fundamental matrix . Both matrices can be used for establishing constraints between matching image points, but the essential matrix can only be used in relation to calibrated .... If, however, the cameras are calibrated the essential matrix can be useful for determining both the relative ... where math mathbf R math is a math 3 times 3 math rotation matrix and math mathbf t math is a 3 dimensional translation vector. Define the essential matrix as style font size 120 border 3px dashed ... product Conversion to matrix multiplication matrix representation of the cross product with math mathbf t math . To see that this definition of the essential matrix describes a constraint on corresponding ... T , mathbf R mathbf I math since math mathbf R math is a rotation matrix. Properties of the Cross product Conversion to matrix multiplication matrix representation of the cross product . Finally, it can ... that the essential matrix defines between corresponding image points. Properties of the essential matrix Not every arbitrary math 3 times 3 math matrix can be an essential matrix for some stereo cameras. To see this notice that it is defined as the matrix product of one rotation matrix and one skew symmetric matrix , both math 3 times 3 math . The skew symmetric matrix must have two singular values which are equal and another which is zero. The multiplication of the rotation matrix does not change ... 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 1980s 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. disambiguation Category Mathematical disambiguation ... 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 knottheory stub ... 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
A DFT matrix is an expression of a discrete Fourier transform DFT as a Matrix mathematics matrix multiplication. Definition An N point DFT is expressed as an N by N matrix multiplication as math X W x math , where math x math is the original input signal, and math X math is the DFT of the signal. The transformation math W math of size math N times N math can be defined as math W left frac omega jk sqrt N right j,k 0, ldots,N 1 math , or equivalently math W frac 1 sqrt N begin bmatrix 1&1&1&1& cdots &1 1& omega& omega 2& omega 3& cdots& omega N 1 1& omega 2& omega 4& omega 6& cdots& omega 2 N 1 1& omega 3& omega 6& omega 9& cdots& omega 3 N 1 vdots& vdots& vdots& vdots&& vdots 1& omega N 1 & omega ... math . This is the Vandermonde matrix for the roots of unity, up to the normalization factor. Note that the normalization ... factors be 1 N . However, the math 1 sqrt N math choice here makes the resulting DFT matrix unitary matrix unitary , which is convenient in many circumstances. Fast Fourier Transform algorithms utilize the symmetries of the matrix to reduce the time of multiplying a vector by this matrix, from ... matrix and the Walsh matrix . Examples Two point The two point DFT is a simple case, in which ... point The four point DFT matrix is as follows math frac 1 2 begin bmatrix 1 & 1 & 1 & 1 1 & i & 1 & i ... 2 math The following image depicts the DFT as a matrix multiplication, with elements of the matrix ... has a fractional frequency of 1 8. In this way, it could be said that the top rows of the matrix ... For other properties of the DFT matrix, including its eigenvalues, connection to convolutions, applications ... image2 Fourieropi.png caption2 Imaginary part sine If we make a very large matrix with complex exponentials ... Fourier operator can be displayed as an image, analogous to the DFT matrix, as shown at right ... The Transform and Data Compression Handbook by P. C. Yip, K. Ramamohan Rao See chapter 2 for a treatment of the DFT based largely on the DFT matrix External links http wearcam.org ece431 course ... 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 with nonpositive off diagonal entries. A Stieltjes matrix is necessarily an M matrix . Every n n Stieltjes matrix is invertible to a nonsingular symmetric nonnegative matrix nonnegative matrix, 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 Numerical linear algebra Category Matrices Category Numerical linear algebra Linear algebra stub sl Stieltjesova matrika ... more details
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