61. Matrices And Linear Algebra - Wolfram Mathematica Mathematica automatically handles both numeric and symbolic matrices, seamlessly switching among large numbers of highlyoptimized algorithms. http://reference.wolfram.com/mathematica/guide/MatricesAndLinearAlgebra.html

baselang='MatricesAndLinearAlgebra.en'; PreloadImages('/common/images2003/link_products_on.gif','/common/images2003/link_purchasing_on.gif','/common/images2003/link_forusers_on.gif','/common/images2003/link_aboutus_on.gif','/common/images2003/link_oursites_on.gif'); DOCUMENTATION CENTER SEARCH Mathematica Mathematics and Algorithms Matrices and Linear Algebra Mathematica automatically handles both numeric and symbolic matrices, seamlessly switching among large numbers of highly-optimized algorithms. Using many original methods, Mathematica can handle numerical matrices of any precision, automatically invoking machine-optimized code when appropriate. Mathematica handles both dense and sparse matrices, and can routinely operate on matrices with millions of entries. automatically operate element-wise: a b c d a c b d Dot scalar dot product Cross Norm Total Normalize ... Table construct a matrix from an expression IdentityMatrix DiagonalMatrix RotationMatrix HilbertMatrix ... Part a part or submatrix: m i j ; resettable with m i j x Dimensions Take Drop Diagonal ... SchurDecomposition Matrix Tests MatrixQ HermitianMatrixQ PositiveDefiniteMatrixQ Displaying Matrices MatrixForm display a matrix in 2D form MatrixPlot visualize a matrix using colors for elements SparseArray construct a sparse matrix from positions and values ArrayRules Normal CoefficientArrays Data Formats "CSV"

62. BLOSUM Matrices The BLOSUM matrices originate with a paper by Henikoff and Henikoff (1992; PNAS 891091510919). Their idea was to get a better measure of differences http://helix.mcmaster.ca/721/distance/node10.html

63. Graph Theory Lesson 7 Look at the adjacency matrices of a few more graphs. Notice that since in our adjacency matrices the diagonal entries are zero aii and ajj are zero so http://www.utc.edu/~cpmawata/petersen/lesson7.htm

Graph Theory Lessons Lesson7: Adjacency Matrices The adjacency matrix of a graph is an n x n matrix A = (a i,j in which the entry a i,j if there is an edge from vertex i to vertex j and is if there is no edge from vertex i to vertex j . By the way, a matrix with only zeros and ones as entries is called a (0,1) matrix. In the applet below draw a few graphs and the applet will display the adjacency matrix of a graph you draw. A graph and its adjacency matrix To use the program Petersen to see the adjacency matrix of a graph , you should first get the program to draw the graph and then click Properties and then Adjacency Matrix Look at the adjacency matrix of the null graphs N , N , N . Describe the adjacency matrix of a null graph. Look at the adjacency matrix of the complete graphs K , K , K . Describe the adjacency matrix of a complete graph. Look at the adjacency matrices of a few more graphs. Give an interpretation for the sum of the entries in row i of an adjacency matrix. Suppose you are told that the adjacency matrix for a simple graph has 5 rows and 5 columns. Suppose you are also told that each row contains three ones and two zeros, why is this impossible?

64. GameDev.net - Vectors And Matrices: A Primer I will teach you two primary things here, Vectors and matrices (with determinants). I m not going to go into everything, so this isn t designed as a http://www.gamedev.net/reference/articles/article1832.asp

Vectors and Matrices: A Primer GameDev.net Vectors and Matrices: A Primer by Phil Dadd Preface Hey there! This tutorial is for those who are new to 3D programming, and need to brush up on that math. I will teach you two primary things here, Vectors and Matrices (with determinants). I'm not going to go into everything, so this isn't designed as a standalone reference. A lot of mathematics books can probably discuss this much better, but anyway, without further ado, lets get on with it shall we? Vectors Vector basics – What is a vector? Vectors are the backbone of games. They are the foundation of graphics, physics modelling, and a number of other things. Vectors can be of any dimension, but are most commonly seen in 2 or 3 dimensions. I will focus on 2D and 3D vectors in this text. Vectors are derived from hyper-numbers, a sub-set of hyper-complex numbers. But enough of that, you just want to know how to use them right? Good. The notation for a vector is that of a bold lower-case letter, like i , or an italic letter with an underscore, like i . I'll use the former in this text. You can write vectors in a number of ways, and I will teach you 2 of them:

65. Tridiagonal And Bidiagonal Matrices Tridiagonal and Bidiagonal matrices. Tridiagonal and Bidiagonal matrices. An unsymmetric tridiagonal matrix of order n is stored in three http://netlib.cs.utk.edu/lapack/lug/node125.html

Next: Unit Triangular Matrices Up: Matrix Storage Schemes Previous: Band Storage Contents Index Tridiagonal and Bidiagonal Matrices An unsymmetric tridiagonal matrix of order n is stored in three one-dimensional arrays, one of length n containing the diagonal elements, and two of length n containing the subdiagonal and superdiagonal elements in elements n A symmetric tridiagonal or bidiagonal matrix is stored in two one-dimensional arrays, one of length n containing the diagonal elements, and one of length n containing the off-diagonal elements. (EISPACK routines store the off-diagonal elements in elements n of a vector of length n Susan Blackford

66. Random Matrices, Related Topics And Applications - CRM, Montreal, August 25 - 30 The mathematics that has been developed for Random Matrix Theory in the past two decades is astonishingly rich and includes variational techniques, http://www.crm.umontreal.ca/Matrices08/index_e.shtml

Housing Contact Home Invited Participants ... Thematic Year The mathematics that has been developed for Random Matrix Theory in the past two decades is astonishingly rich and includes variational techniques, inverse spectral approach to nonlinear integrable differential and difference systems, new asymptotic techniques, such as the nonlinear steepest descent method, free probability and large deviations methods. The results obtained have found new applications in a stunningly wide range of areas of both mathematics and theoretical physics such as, for example, approximation theory, orthogonal polynomials and their asymptotics, number theory, combinatorics, dynamical systems of integrable type, representation theory of finite and infinite groups, growth phenomena, quantum gravity, conformal field theory, supersymmetric Yang-Mills theory and string theory. This workshop will focus on recent advances in the asymptotic spectral theory of random matrices, connections with (multi-)orthogonal polynomials, combinatorics and moduli space theory of Riemann surfaces, algebraic geometry, theory of isomonodromic deformations, number theory and Dyson processes. Scientific Organizers E. Basor

67. Formulas For Stress, Strain, And Structural Matrices (2nd Edition) The most comprehensive book in its field, this book is a source of formulas for the analysis and design of structural members and mechanical elements. http://www.knovel.com/knovel2/Toc.jsp?BookID=1429

68. The Matrix Market Matrices By Name The Matrix Market. matrices by Name. Use this list if you already know the name of the matrix you want; otherwise, go to Search. http://math.nist.gov/MatrixMarket/matrices.html

Matrices by Name Use this list if you already know the name of the matrix you want; otherwise, go to Search 1138 BUS 494 BUS 662 BUS ... ZENIOS The Matrix Market is a service of the Mathematical and Computational Sciences Division Information Technology Laboratory National Institute of Standards and Technology Home ... Resources Last change in this page: Tue May 14 17:10:06 US/Eastern 2002 [Comments: matrixmarket nist.gov

69. Essential And Fundamental Matrices Then the matrices A1 and A2 (from (4)) containing the internal parameters of the two cameras are needed to transform the normalized coordinates into pixel http://vision.stanford.edu/~birch/projective/node20.html

Next: Alternate derivation: algebraic Up: Projective Geometry Applied to Previous: Image formation Essential and fundamental matrices Suppose we have a stereo pair of cameras viewing a point in the world which projects onto the two image planes at and (Since we are dealing with homogeneous coordinates, is , and and are each ). If we assume the cameras are calibrated, then and are given in normalized coordinates , that is, each is given with respect to its camera's coordinate frame. The epipolar constraint says that the vector from the first camera's optical center to the first imaged point, the vector from the second optical center to the second imaged point, and the vector from one optical center to the other are all coplanar. In normalized coordinates, this constraint can be expressed simply as where R and capture the rotation and translation between the two cameras' coordinate frames. The multiplication by R is necessary to transform into the second camera's coordinate frame. By defining as the matrix such that for any vector we can rewrite the equation as a linear equation: where is called the Essential matrix and has been studied extensively over the last two decades.

70. MATLAB - Images And Matrices Demo This demo illustrates this idea of representing a matrix as an image and in general displaying images stored as matrices. http://www.mathworks.com/products/matlab/demos.html?file=/products/demos/shippin

71. Matrices Help Relationships matrices Help Relationships. matrices Help Relationships; matrices Help Relationships An Airline Problem. Copyright © 19962008 Alexander Bogomolny http://www.cut-the-knot.org/blue/relation.shtml

var MyPageLoc = document.location; var MyPageTitle = document.title; G o o g ... e Web CTK Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Matrices Help Relationships William A. McWorter Jr. Once when I was a graduate student I had a conversation with a philosophy professor friend about epistomology. He said there is a problem with the referent theory of meaning. The planet Venus and the Morning Star have the same referent, the planet, but the phrases clearly have different meanings. Being a student of mathematics, I had recently learned that mathematicians treat relationships as objects like any other object. So I suggested "why not include relationships as referents?". Then the Morning Star would have as one of its referents the relationship between Venus and the morning, distinguishing that phrase from the planet Venus. The philospher said "then the universe would have too many objects". Not long after that I gave up on philosophy. It seemed to me that philosphers were not interested in the truth. They prefer to haggle endlessly over dilemmas. This same relationship can be recorded as a matrix. Label the rows and columns of matrix by E, J, and P. Place a 1 in a cell of the matrix provided the row label of the cell is related to the column label of that cell. Put zeros in all other cells of the matrix.

72. Hermitian Matrices Notice that the matrix A can be written as the sum AR + iAI where AR and AI are real valued matrices. The complex conjugate of A can then be written in the http://www.mathpages.com/home/kmath306/kmath306.htm

Hermitian Matrices Given a matrix A of dimension m k (where m denotes the number of rows and k denotes the number of columns) and a matrix B of dimension k n, the matrix product AB is defined as the m n matrix with the components for m ranging from 1 to m and for n ranging from 1 to n. Notice that matrix multiplication is not generally commutative, i.e., the product AB is not generally equal to the product BA. The transpose A T of the matrix A is defined as the k m matrix with the components for m ranging from 1 to m and for k ranging from 1 to k. Notice that transposition is distributive, i.e., we have (A+B) T = (A T + B T Combining the preceding definitions, the transpose of the matrix product AB has the components Hence we've shown that We can also define the complex conjugate A of the matrix A as the m k matrix with the components Notice that the matrix A can be written as the sum A R + iA I where A R and A I are real valued matrices. The complex conjugate of A can then be written in the form We also note that transposition and complex conjugation are commutative, i.e., we have (A T = (A T . Hence the composition of these two operations (in either order) gives the same result, called the

73. Vectors And Matrices It is slow at evaluating expressions, and provides no facility for handling vectors or matrices. Since the latter two are needed for structure analysis, http://www.ks.uiuc.edu/Research/vmd/current/ug/node176.html

Next: Vectors Up: VMD User's Guide Previous: Saving and Restoring Molecule Contents Index Vectors and Matrices Tcl does not handle mathematical expressions very well. It is slow at evaluating expressions, and provides no facility for handling vectors or matrices. Since the latter two are needed for structure analysis, we have added routines to manipulate them. A vector in VMD is a list of numbers. All of the vector routines but one will work with vectors of any length; veccross will only use vectors of three numbers. A matrix is a 4x4 collection of numbers stored as a list of 4 vectors of 4 numbers, in row-major form. Following are descriptions and examples of all the commands. For more examples of vectors, though without much documentation, the script used to test the vectors implementation is located at $env(VMDDIR)/scripts/vmd/test-vectors.tcl Since Tcl is slow at math, some of these commands have been reimplemented in C++. (The original definition is in the vmd script distribution, but it is redefined later on inside VMD). At times, the speedup is a factor of 40 or more. These commands are noted by (C++). Subsections Vectors Matrix routines Multiplying vectors and matrices Misc. functions and values

74. Sparse Matrices In MATLAB Design And Implementation - Gilbert We have extended the matrix computation language and environment MATLAB to include sparse matrix storage and operations. The only change to the outward http://citeseer.ist.psu.edu/gilbert91sparse.html

75. 2.10.2 Matrices There are a variety of other commands that manipulate matrices. Rotate , Translate , Scale , Frustum , and Ortho manipulate the current matrix. http://www.opengl.org/documentation/specs/version1.1/glspec1.1/node25.html

Next: 2.10.3 Normal Transformation Up: 2.10 Coordinate Transformations Previous: 2.10.1 Controlling the Viewport 2.10.2 Matrices The projection matrix and model-view matrix are set and modified with a variety of commands. The affected matrix is determined by the current matrix mode. The current matrix mode is set with void MatrixMode enum mode which takes one of the three pre-defined constants TEXTURE MODELVIEW , or PROJECTION as the argument value. TEXTURE is described later. If the current matrix mode is MODELVIEW , then matrix operations apply to the model-view matrix; if PROJECTION , then they apply to the projection matrix. The two basic commands for affecting the current matrix are void LoadMatrix[fd] T m[16] void MultMatrix[fd] T m[16] LoadMatrix takes a pointer to a matrix stored in column-major order as 16 consecutive floating-point values, i.e. as (This differs from the standard row-major C ordering for matrix elements. If the standard ordering is used, all of the subsequent transformation equations are transposed, and the columns representing vectors become rows.) The specified matrix replaces the current matrix with the one pointed to.

76. Introduction To Matrices / Matrix Size Defines matrices and basic matrix terms, illustrating these terms with worked solutions to typical homework exercises. http://www.purplemath.com/modules/matrices.htm

powered by FreeFind Print-friendly page Introduction to Matrices / Matrix Size (page 1 of 3) Matrix equality Augmented matrices Matrices are incredibly useful things that crop up in many different applied areas. For now, though, you'll probably only do some elementary manipulations with matrices, and then you'll move on to the next topic. But you should not be surprised to encounter matrices again in, say, physics or engineering. Matrices were initially based on systems of linear equations. For instance: Given the following system of equations, write the associated augmented matrix. x y z x y z x y z Write down the coefficients and the answer values, including all "minus" signs. If there is "no" coefficient, then the coefficient is " ". That is, given a system of (linear) equations, you can relate to it the matrix (the grid of numbers inside the brackets) which contains only the coefficients of the linear system. This is called "an augmented matrix". The entries of (that is, the values in) the matrix correspond to the

77. Matrices - Screenshots - Calc 3D Calc 3D is a calculator for vectors, matrices, complex numbers, coordinates, intersections and function plotting (polar plot,2D,3D). http://www.calc3d.com/tour/etour8.html

Screenshots: Matrices Back Next Screenshots Editor Plot Function Polar Plot Best fit ... Vector Matrices 2 Points Line - Circle Plane - Line Coordinates ... Features Screenshots Download Help Online help Online calculators ... Features Screenshots Download Help Online help Online calculators ... and Andreas Greuer

78. Hadamard Matrices In my recent paper on Hadamard matrices of orders 24 and 28 that appeared in Discrete Math. 140 (1995) 185243 , I also repeated this erroneous figure. http://www.maths.gla.ac.uk/~es/hadamard.html

Hadamard matrices It has been a common misapprehension over the last seven or eight years that the number of pairwise non-isomorphic 2-(23,11,5) designs is 1102. This notion was first put forward by H. Kimura (New Hadamard matrix of order 24, Graphs Combin. (1986) 247-257) who found a Hadamard matrix of order 24 that had been missed by Ito et al (Classification of 3-(24,12,5) designs and 24-dimensional Hadamard matrices, J. Comb. Theory Ser. A 27 (1979) 289-306). It is a figure that appears even today in the new CRC Handbook of Combinatorial Designs. In my recent paper on Hadamard matrices of orders 24 and 28 that appeared in Discrete Math. (1995) 185-243 , I also repeated this erroneous figure. Had I bothered to check the numbers of Hadamard designs that I had found from the 60 Hadamard matrices of order 24, I would have announced that the correct number of pairwise non-isomorphic 2-(23,11,5) designs is . This number is implicit in the Table on pp 192-196 appearing in my paper cited above, and indeed all 1106 designs are contained in each of the files 23-11-5.gz* above. Some people may be interested in having the electronic copies of the Hadamard matrices of orders up to 28. Since they are unique for orders 2, 4, 8 and 12, I only list those of orders 16, 20, 24 and 28. These can be found in the files

79. IFTA - Fuel Tax Rates www.iftach.org/taxmatrix2/choose_table.php Similar pages Earliest Uses of Symbols for matrices and VectorsMost of the basic notation for matrices and vectors in use today was available by the early 20th century. Its development is traced in volume 2 of Florian http://www.iftach.org/taxmatrix2/choose_table.php

IFTA - Fuel Tax Rates Please select the quarter you want to view, print, or download. View, Print, or Download Tax Matrices for * = Inactive Table For Tax Matrices previous to 2003 click here All users of the information contained in this web page understand and agree that IFTA, Inc. is not responsible for the accuracy of the information provided to IFTA, Inc. by the Member Jurisdictions. All information contained in this web page is reported to IFTA, Inc. by the Member Jurisdictions, and IFTA, Inc. does not alter the information reported by the Member Jurisdictions or independently confirm the accuracy of the information reported by the Member Jurisdictions. Each Member Jurisdiction is solely responsible for the information reported to IFTA, Inc. that is posted in this web page. Additionally, each Member Jurisdiction is also solely responsible for updating the information reported by them to assure that it remains accurate. Any inquiries or disputes concerning the accuracy of the information contained in this web page must be directed to the Member Jurisdiction responsible for reporting the information in question. Close

80. Open Question: Deterministic UUP Matrices « What’s New I will define exactly what UUP matrices (the UUP stands for “uniform uncertainty principle“) are later in this post. For now, let us just say that they are http://terrytao.wordpress.com/2007/07/02/open-question-deterministic-uup-matrice

var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E")); Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao Home About Career advice On writing ... Subscribe to feed Open question: deterministic UUP matrices 2 July, 2007 in math.MG math.NA question Tags: compressed sensing derandomisation random matrices RIP ... UUP This problem in compressed sensing is an example of a derandomisation problem : take an object which, currently, can only be constructed efficiently by a probabilistic method, and figure out a deterministic construction of comparable strength and practicality. (For a general comparison of probabilistic and deterministic algorithms, I can point you to these slides by Avi Wigderson uniform uncertainty principle orthogonal matrices , in which the columns are locally almost orthogonal rather than globally perfectly orthogonal. Because of this, it turns out that one can pack significantly more columns into a UUP matrix than an orthogonal matrix, while still capturing many of the desirable features of orthogonal matrices, such as stable and computable invertibility (as long as one restricts attention to sparse or compressible by de Vore for UUP matrices with small sparsity parameter.

Page 4     61-80 of 81    Back | 1  | 2  | 3  | 4  | 5  | Next 20