61. Matrices matrices are perhaps the most common data type in Macaulay 2. making matrices. input a matrix random and generic matrices concatenating matrices http://www.math.uiuc.edu/Macaulay2/Manual/1425.html

search for: matrices An overview In Macaulay 2, each matrix is defined over a ring, (see rings ). Matrices are perhaps the most common data type in Macaulay 2. making matrices input a matrix random and generic matrices concatenating matrices operations involving matrices simple information about a matrix basic arithmetic of matrices kernel, cokernel and image of a matrix differentiation determinants and related computations rank of a matrix determinants and minors Pfaffians exterior power of a matrix display of matrices and saving matrices to a file format and display of matrices in Macaulay 2 importing and exporting matrices For an overview of matrices as homomorphisms between modules, see modules I . For additional common operations and a comprehensive list of all routines in Macaulay 2 which return or use matrices, see Matrix search for:

62. Computational Physics -- 3rd/4th Year Option Course covers quantifying techniques that are used in physics. Topics include ordinary differential equations, partial differential equations, matrices, and simulation methods. http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/

Next: Computational Physics Course Description Computational Physics 3rd/4th Year Option Angus MacKinnon An Adobe Acrobat (PDF) version of this document is available. Computational Physics Course Description Ordinary Differential Equations Types of Differential Equation ... Bibliography

63. PAM Matrices PAM matrices. There are several common ways in which weights can be applied for amino acid differences. This results in a family of scoring matrices. http://helix.biology.mcmaster.ca/721/distance/node9.html

Next: BLOSUM Matrices Up: Amino acid distance Previous: Amino acid distance PAM Matrices There are several common ways in which weights can be applied for amino acid differences. Karlin and Ghandour (1985, PNAS 82:8597) proposed a method of weights based on chemical, functional, charge and structural properties of the amino acids. Similarly Doolittle proposed weights based on the structural similarities and the ease of genetic interchange (Feng et al ., 1985 J. Mol. Evol. 21: 112). However, by far the most common and most famous way to assign weights is to use Dayhoff's PAM250 matrix. This is a matrix of weights that is derived from how often different amino acids replace other amino acids in evolution (see M.O. Dayhoff, ed., 1978, Atlas of Protein Sequence and Structure, Vol5). This was based on a data base of 1,572 changes in 71 groups of closely related proteins appearing in earlier volumes of this amazing predecessor to electronic databases. PAM stands for percent accepted mutations and these were inferred from the types of changes observed in these proteins. Every change was tabulated and entered in a matrix enumerating all possible amino acid changes. In addition to these counts of accepted point mutations an idea of the relative mutability of different amino acids were calculated. The information about the individual kinds of mutations and about the relative mutability of the amino acids can be combined into one distance-dependent "mutation probability matrix". The elements of this matrix give the probability that the amino acid in one column will be replaced by the amino acid in some row after a given evolutionary interval. For example, a matrix with an evolutionary distance of PAMs would have ones on the main diagonal and zeros elsewhere. A matrix with an evolutionary distance of

64. BLOSUM Matrices The BLOSUM matrices originate with a paper by Henikoff and Henikoff (1992; While this bias limits the usefulness of BLOSUM matrices for some purposes, http://helix.biology.mcmaster.ca/721/distance/node10.html

Next: GAP WEIGHTING Up: Amino acid distance Previous: PAM Matrices BLOSUM Matrices The BLOSUM matrices originate with a paper by Henikoff and Henikoff (1992; PNAS 89:10915-10919). Their idea was to get a better measure of differences between two proteins specifically for more distantly related proteins. While this bias limits the usefulness of BLOSUM matrices for some purposes, for other programs such as FASTA, BLAST, etc. it should do substantially better. This is because the need for an accurate measure of distance is not as great when peptides are more closely related. They use the BLOCKS database to search for differences among sequences but only among the very conserved regions of a protein family. Hence the term BLOSUM is from BLOcks SUbstitution Matrix. They first collect all of the sequences in the BLOCKS database and then for each one they sum the number of amino acids in each site to get a frequency table ( ) of how often different pairs of amino acids are found together in these conserved regions. Hence the observed frequency of occurrence of one amino acid is Given pairs should occur with frequencies and The odds matrix is . Generally 's are taken of this matrix to give a or lod matrix such that Hence if the observed number of differences between a pair of amino acids is equal to the expected number than . If the observed is less than expected then and if the observed is greater than expected All of this gives the BLOSUM matrix. Different levels of the BLOSUM matrix can be created by differentially weighting the degree of similarity between sequences. For example, a BLOSUM62 matrix is calculated from protein blocks such that if two sequences are more than 62% identical, then the contribution of these sequences is weighted to sum to one. In this way the contributions of multiple entries of closely related sequences is reduced.

65. Peanut Software Homepage Free mathematics software for Windows. Individual software packages handle geometry, equations, statistics, discrete math, fractals, matrices, and games. http://math.exeter.edu/rparris/default.html

Peanut Software Homepage Last Updated: 15 Sept 2005 There is a mirror site , which contains the same current versions as this site. There is also a page of FAQ (16 Jun 2005), which I will add to as necessary. Generous Peanut users have established a mailing list and a database for sharing documents. Click the following links to reach the download pages: Wingeom (15 Sep 2005) Winplot (16 Aug 2005) Winstats (28 Jun 2005) Winarc (14 Sep 2005) Winfeed (14 Mar 2005) Windisc (19 Mar 2005) Winlab (07 Jul 2000) Winmat (31 Jan 2005) Wincalc (02 Mar 2005) Documents (15 Sept 2005) The programs may be freely distributed, and the author ( rparris@exeter.edu ) welcomes suggestions for improvements and repairs. Current versions (dated with the program) are always available at this site (Phillips Exeter Academy). Each downloaded program is a self-extracting archive, which contains the executable file and perhaps some accessory files. The executable file includes documentation that can be printed, exported to your word processor, or simply used for on-screen help. To download programs, first create a directory on your hard drive into which the files will be copied, then click the desired links. After downloading, execute each file (double-click its icon) to extract its contents. The program icon should now appear in the directory window. There is no installation program — you will have to

66. Matrices We now turn to some definitions and properties of matrices and operations on matrices. Square matrix If A has the same number of rows as columns, http://cepa.newschool.edu/het/essays/math/matrix.htm

Matrices Back A matrix A is a rectangular array of numbers, coefficients or variables. A (n m)-dimensional matrix has n rows and m columns. A vector x is a particular type of matrix with only one column, i.e. if x is a (n 1) matrix, then x is a n-dimensional vector. Thus: a a a a a a A a a a nm and: x x x x n are examples of a matrix ( A ) and a vector ( x ). We can denote a matrix A by its typical element , thus A = [a ij ], where i = 1, ..., n; j = 1, ..., m. We now turn to some definitions and properties of matrices and operations on matrices. Square matrix : If A has the same number of rows as columns, we refer to it as a square matrix. Matrix addition A B - elements are added correspondingly, so A B = [a ij + b ij ]. This requires that A and B have same dimensions. It is clear that the following properties hold: (i) A B B A (ii) ( A B C A B C Scalar multiplication a A - every element is multiplied by scalar a , thus a A a a ij Matrix multiplication AB - uses procedure whereby a typical element of AB , call it c ij , is obtained by the summation of the products of the ith row of A (call it a i ) and the jth column of B (call it b j ). Thus, c

67. PSPASES Home Page High performance, scalable, parallel, MPIbased library, intended for solving linear systems of equations involving sparse symmetric positive definite matrices. The library provides various interfaces to solve the system using four phases of direct method of solution compute fill-reducing ordering, perform symbolic factorization, compute numerical factorization, and solve triangular systems of equations. http://www-users.cs.umn.edu/~mjoshi/pspases/index.html

PSPASES Home Software Publications People Feedback PSPASES (Parallel SPArse Symmetric dirEct Solver) is a high performance, scalable, parallel, MPI-based library, intended for solving linear systems of equations involving sparse symmetric positive definite matrices. The library provides various interfaces to solve the system using four phases of direct method of solution : compute fill-reducing ordering, perform symbolic factorization, compute numerical factorization, and solve triangular systems of equations. The library efficiently implements the scalable parallel algorithms developed by the authors, to compute each of the phases [ GKK JGKK GGJKK KK Features: High Performance Library. Solved a million equation system in 154 seconds on Cray T3E with most computationally intensive phase clocking at 52 GFLOPS! Portable to most of today's parallel computers. Tested on IBM, Cray, and SGI platforms. Entirely parallel and scalable code. Each of the four phases is parallelized. Library functions can be called from both C and Fortran 90 codes, with simple calling sequences. Memory requirements for the numerical factorization phase can be pre-estimated.

68. Mkaz.com : Matrices - The Mathematics Behind Them mkaz.com Linear Algebra Calculators. Do online matrix calculations, such as determinant, inverse, solve system of three equations and more http://www.mkaz.com/math/math35.html

mkaz.com blog photography personal web dev ... about Matrices - The Mathematics Behind Them Let A B , and C represent n x n matrices. Example of a 3 x 3 Matrix: A B C The addition of two matrices is straight forward. You just add each matrix position-wise. So the upper-left element of matrix A plus the upper-left element of matrix B is the upper-left element in matrix C . Do the same for all elements. A x B C The multiplication of two matrices is not quite as simple. First we need the matrices to be of proper size. This means matrix A size n x m must be multiplied by a m x p matrix. The resultant matrix will then be n x p . For our case, we are using n x n matrices, so this isn't a problem. The equation for multiplying two matrices is : (elementwise) AB ij SIGMA A ik B kj where the SIGMA summation goes from k=1...n A example element from our 3x3 Case. To get the first element in our solution matrix c c = (a * b ) + (a * b ) + (a * b where a ij and b ij are from matrices A B respectively. trace( A The trace of a matrix is simply the summation of its main diagonal. A T The transpose of a matrix is switching the rows and colums. For example:

69. Ted Spence's Home Page Classification of Hadamard matrices and designs. http://www.maths.gla.ac.uk/~es/

My research interests at the present time are in the area of classification of combinatorial designs of various different sorts. In some cases I have been able to classify the designs completely and where this has been possible I have stored the designs on disc. They can be accessed via the Table below. These files will be updated at intervals, as I find the time. no (81,16,3) design could be constructed with the above assumptions . The reason that I announce this here is to save a fellow researcher from spending some time on what has turned out to be a fruitless task. If you do download any of my files, it would be appreciated if you would e-mail me a message to let me know that you have done so: ted@maths.gla.ac.uk List of Publications 2-designs Hadamard matrices ... Symmetric designs with a non-null polarity Department of Mathematics University of Glasgow Glasgow G12 8QQ SCOTLAND

70. MHC Class I Binding Peptide Prediction Server List of matrices used by the ProPred1 server. Source of matrices. matrices name, Type of matrices, Source of Information http://www.imtech.res.in/raghava/propred1/matrices/matrix.html

71. Workshop On L-functions And Random Matrices May 1418, 2001, American Institute of Mathematics, Palo Alto, California. http://www.aimath.org/projects/rmt_wkshp.html

WORKSHOP ON L-FUNCTIONS AND RANDOM MATRICES WHERE: American Institute of Mathematics (AIM), Palo Alto, CA DATES: Monday, May 14 - Friday, May 18, 2001 ORGANIZER: Brian Conrey (conrey@aimath.org) List of Participants Some open problems Schedule of talks Hotels where everyone is staying DESCRIPTION: In 1974, H. Montgomery found the first indication of a connection between the distribution of the zeros of the Riemann zeta-function and the distribution of the eigenvalues of random matrices. Random matrices had been studied by statisticians beginning in the 1930s and Mathematical Physicists starting in the 1950s. In 1981, numerical calculations by A. Odlyzko of some statistics of the zeros of the Riemann zeta-function led to remarkable graphs illustrating the connection that Montgomery predicted. Recent work by many authors, has led to several interesting developments including the study of low lying zeros of families of L-functions and conjectures for mean-values of L-functions running in a family. The purpose of this workshop is to consider the future development of this field, with a focus on understanding the goals of the subject, the limitations, and how to attack the important unsolved problems.

72. Matrices As Linear Transformations matrices can be interpreted as linear transformations of the plane. When you multiply a matrix by a vector you obtain a new vector which, in general, http://www.maths.soton.ac.uk/~cjh/ma156/matrices/matrices.html

Faculty of Mathematical Studies University of Southampton Mathematical methods for Physical Sciences Matrices as linear transformations of the plane Matrices can be interpreted as linear transformations of the plane. When you multiply a matrix by a vector you obtain a new vector which, in general, has a different length and a different direction from the original. If we apply a 2x2 matrix to the position vectors of the vertices of a polygon in the xy coordinate plane, we can expect that the polygon will be deformed as the position vectors of its vertices are stretched and rotated. If you click here you can download an Excel spreadsheet (courtesy of Dr Keith Hirst) that will help you understand how matrices can be used to describe linear transformations of figures in the plane. Click here to download the matrix spreadsheet. Click here to get a brief introduction to Excel.

73. INI Programme Isaac Newton Institute, Cambridge, UK; 1821 May 2004. http://www.newton.cam.ac.uk/programmes/RMA/rmaw03.html

An Isaac Newton Institute Workshop Satellite workshop on Random Matrices and Probability 18 - 21 May 2004 Organisers F Mezzadri ( Bristol ), N O'Connell ( Warwick ) and NC Snaith ( Bristol Supported by The London Mathematical Society (LMS) in association with the Newton Institute programme entitled Random Matrix Approaches in Number Theory Theme of Conference: Random Matrix theory was first developed in the 1950s by Wigner, Dyson and Metha to describe the spectra of highly excited nuclei. Since then it has found application in many branches of Mathematics and Physics, from quantum field theory to condensed matter physics, quantum chaos, operator algebra, number theory and statistical mechanics. This workshop will focus on those aspects of random matrix theory that find application in probability. Specific themes will include: a) Brownian motion and the Riemann zeta function; b) Eigenvalues of non-Hermitian random matrices; c) Universality, sparse random matrices, transition matrices and stochastic unitary matrices; d) Matrix-valued diffusion, Brownian motion on symmetric spaces; e) Intertwining relationships in random matrix theory and quantum Markov processes. Confirmed participants D. Applebaum (

74. MathHelp Notebook On Matrices http://www.ucl.ac.uk/Mathematics/geomath/level2/mat/MHma.html

75. MATRIX04 - The 13th International Workshop On Matrieces And Statistics The 13th International Workshop on matrices and Statistics. Bªdlewo, Poland; 1821 August 2004. http://matrix04.amu.edu.pl/

Welcome The 13th International Workshop on Matrices and Statistics (IWMS-2004) will be held in Bêdlewo, about 30 km south of Poznañ, Poland, from 18th by 21st August 2004. Bêdlewo is the Mathematical Research and Conference Center of the Polish Academy of Sciences; the setting is similar to Oberwolfach, with accommodation on site. For further information about this place please visit the Web site www.impan.gov.pl/Bedlewo/ Poznañ is one of the oldest cities and the greatest academic centers in Poland. It has over half million inhabitants and it is located about 300 km west of Warsaw. There is an airport which offers a number of international connections. Nokia Lecturer at the IWMS-2004 The organizers of the Bêdlewo Matrix Workshop are very pleased to announce that the Finnish-based company Nokia will sponsor the Workshop, in a form of the Nokia Lectureship Program for IWMS-2004.

76. The Math Forum - Math Library - Matrices The Math Forum s Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites http://mathforum.org/library/topics/matrices/

Browse and Search the Library Home Math Topics Algebra Linear Algebra : Matrices Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Linear and Multilinear Algebra; Matrix Theory (Finite and Infinite) - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to linear and multilinear algebra and matrix theory. As presented to engineers and as the subject of much numerical analysis, this subject is Matrix Theory. To an algebraist or geometer, it is the theory of Vector Spaces. Linear algebra, sometimes disguised as matrix theory, considers sets and functions which preserve linear structure. In practice this includes a very wide portion of mathematics; thus linear algebra includes axiomatic treatments, computational matters, algebraic structures, and even parts of geometry; moreover, it provides tools used for analyzing differential equations, statistical processes, and even physical phenomena. History, applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> Matrices and Determinants - MacTutor Math History Archives Linked essay describing the history of matrices and determinants from the 2nd century B.C. through the early 20th century, with 13 references (books/articles).

77. Index Small business mobile service aiming to provide experienced, innovative and cost effective analysis organics and inorganics for all matrices map showing ten US offices including Hawaii. http://esnnorth.com/

ESN North Atlantic is.. Our network.. Interactive program Direct Push ESN North Atlantic is.. Our network.. Interactive program Direct Push ... Links

78. Quizz Matrices elementary questions on matrices. interactive exercises, online calculators and plotters, mathematical recreation and games. http://math.cochise.edu/wims/wims.cgi?lang=en& module=U1/algebra/quizmatrix.en

79. OEF Matrices collection of exercises on matrices. interactive exercises, online calculators and plotters, mathematical recreation and games. http://math.cochise.edu/wims/wims.cgi?lang=en& module=U1/algebra/oefmatrix.en

80. Algebra Binary Calculus Logic Graphical Calculator Integrated mathematical tool that can compute mathematical expressions involving complex numbers, polynomials, rational functions, vectors, and matrices. http://www.mathedusoft.com/

MathEduSoft Send a fax online with FaxIt Nice Open an online store with OrderIt Nice What Is Advantix Calculator? For more information on what Advantix Calculator can do, please take a look at the topic: Advantix Calculator Overview. Advantix Calculator Overview Order Advantix Calculator Online Download Advantix Calculator (Free Fully Functional Trial Version) Advantix Distributor Wanted ... Advantix Calculator's Bug Report Last Update: 10/20/99

Page 4     61-80 of 190    Back | 1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | 10  | Next 20