41. Matrices' | Define Matrices' At Dictionary.com , ma trix es. 1. something that constitutes the place or point from which something else originates, takes form, or develops The GrecoRoman world was the matrix for http://dictionary.reference.com/browse/matrices'

42. 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 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

43. Leaving Cert. Higher Level Maths - Matrices Index of applets from the matrices section of the TCD leaving cert higher level maths website. http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/matrices/

Search for: in Entire website Algebra Complex Numbers Matrices Sequences and series Differentiation Integration Circle Vectors Linear Transformations Line Geometry Trigonometry Probability Further Calculus and Series Website Home Algebra Complex Numbers Matrices ... Integration You are here: Home Category Index / Matrices Matrices Algebra Of Matrices - By Mary Glackin The applet will add, subtract or multiply matrices. As division of matrices belongs to matrix inversion that is being dealt with in another applet.Because addition and subtraction of matrices require the matrices to be the same size e.g.2*2 and multiplication requires the no. of rows in one matrix to correspond with the number of columns in the other e.g. 2*2 and 2*2 or 2*3 and 3*2, I decided to use 2*2 matrices for both . This way (a) the applet would be less cluttered and therefore easier to understand , and (b) if somebody understands how to multiply a 2*2 matrix works it is an easy step to go from there to larger matrices . [ View Applet Matrix Equations - By Ciaran Levingston This Applet Explains How To Solve Equations Containing Matrices. It Will Take In Values From The User And Guide You Through The Solution Of That Particular Problem Step By Step. This Applet Uses Simple 1 By 2 Matrices (one Column By Two Rows) To Illustrate The Principal Behind The Solution But The Same Method Can Be Used To Solve Problems Involving Larger Matrices And Problems Involving More Unknowns. [

44. The Datamology Company Exploratory data analysis (EDA) application for Windows. Uses plots such as Box Array, Box Plot, Quantile Array, Scatter Plots (2D, 3D and matrices), and Time-Series (Arrays and matrices). EDA findings can be saved and revisited using a visual library. Full functionality shareware except for publication capabilities, which must be purchased. http://www.datamology.com/

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45. Hadamard Matrices by NJA Sloane Cited by 35 - Related articles http://www2.research.att.com/~njas/hadamard/

A Library of Hadamard Matrices N. J. A. Sloane Keywords : Hadamard matrices, Kimura matrices Paley matrices, Plackett-Burman designs, Sylvester matrices, Turyn construction, Williamson construction Contains all Hadamard matrices of orders n up through 28, and at least one of every order n up through 256. This library is maintained by N. J. A. Sloane njas@research.att.com Notation: had.n.name indicates a Hadamard matrix of order n and type "name". The matrices are usually given as n rows each containing n +'s and -'s (with no spaces). In many cases there are further rows giving the name of the matrix and the order of its automorphism group. What the suffixes mean: od = orthogonal design construction method pal = first Paley type pal2 = second Paley type syl = Sylvester type tur = Turyn type tx = tensor product of type x with ++/+- or (rarely) with a Hadamard matrix of order 4 will = Williamson type References: Seberry, J. and Yamada, M., Hadamard matrices, sequences, and block designs , pp. 431-560 of Dinitz, J. H. and Stinson, D. R., editors (1992), Contemporary Design Theory: A Collection of Essays, Wiley, New York. Chapter 7 of Orthogonal Arrays by Hedayat, Sloane and Stufken.

46. FCCR A working paper on FCCR nxn matrices as local kinematical replacement for CCR, and representations by pxp matrices over Galois fields. http://graham.main.nc.us/~bhammel/FCCR/fccr.html

Finite Canonical Commutation Relations You can never solve a problem on the level on which it was created. Albert Einstein (1879-1955) "Silence will save me from being wrong (and foolish), but it will also deprive me of the possibility of being right. Igor Stravinsky, composer (1882-1971) A working paper on FCCR nxn matricies as local kinematical replacement for CCR, and construction of REPS of CCR by pxp matricies over Galois fields. Some remaining text of the chapters is still being translated to hypertext. An abstract and a brief summary of the essentials are available. The central object of interest here is a chain of algebras given in terms of nxn complex matricies that connect the quantum mechanical Canonical Commutation Relations (CCR) for n unbounded with the Canonical Anticommutation Relations (CAR) for n=2, which seem to provide a local, finite, discrete quantum theory. Finite dimensional representations of CCR by matricies over Galois fields are constructed in appendix J. The detail of mathematics, physics and philosophy presented here is far more than what would be usual in an any professional journal. I believe it to be sufficient that any mathematician/physicist should be able to reproduce and confirm (or correct!) every detail in the exposition.

47. Substitution Matrices Feb 24, 2000 All BLOSUM matrices are based on observed alignments; they are not extrapolated from comparisons of closely related proteins. http://www.ncbi.nlm.nih.gov/Education/BLASTinfo/Scoring2.html

Scoring Systems Log-odds Substitution Matrices for Scoring Amino-Acid Alignments BLOSUM62 Substitution Scoring Matrix . The BLOSUM 62 matrix shown here is a 20 x 20 matrix of which a section is shown here in which every possible identity and substitution is assigned a score based on the observed frequencies of such occurences in alignments of related proteins. Identities are assigned the most positive scores. Frequently observed substitutions also receive positive scores and seldom observed substitutions are given negative scores. The PAM family PAM matrices are based on global alignments of closely related proteins. The PAM1 is the matrix calculated from comparisons of sequences with no more than 1% divergence. Other PAM matrices are extrapolated from PAM1. The BLOSUM family BLOSUM matrices are based on local alignments. BLOSUM 62 is a matrix calculated from comparisons of sequences with no less than 62% divergence. All BLOSUM matrices are based on observed alignments; they are not extrapolated from comparisons of closely related proteins. BLOSUM 62 is the default matrix in BLAST 2.0. Though it is tailored for comparisons of moderately distant proteins, it performs well in detecting closer relationships. A search for distant relatives may be more sensitive with a different matrix.

48. Nick Higham - The Matrix Computation Toolbox free A collection of MATLAB M-files containing functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search optimization. http://www.maths.man.ac.uk/~higham/mctoolbox/

You are here: mathematics staff nick higham Nick Higham ... staff list NEWS Photos of Calculating Careers 2010 Call for papers for 15th Leslie Fox Prize. First Manchester SIAM Student Chapter Conference: photos CICADA Newsletter 3 iPhoneography: The University of Manchester Now on Opportunities: postdoc postgrad Website by Hykel Hosni read archived news The Matrix Computation Toolbox The Matrix Computation Toolbox is a collection of MATLAB M-files containing functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search optimization. Various other miscellaneous functions are also included. This toolbox supersedes the author's earlier Test Matrix Toolbox (final release 1995). The toolbox was developed in conjunction with the book Accuracy and Stability of Numerical Algorithms SIAM Second edition , August 2002, xxx+680 pp.). That book is the primary documentation for the toolbox: it describes much of the underlying mathematics and many of the algorithms and matrices (it also describes many of the matrices provided by MATLAB's gallery function).

49. Lenovo Support & Downloads - Driver Matrices (Most Common Files) Aug 23, 2009 Driver matrices (Most common files) Quick links. Driver matrices Personal Systems Reference (PSREF) http://www-307.ibm.com/pc/support/site.wss/drvr-matrix.html

Country / region Select English Change Home Products My account ... Search PC support Related links Accessories and upgrades Business Partner support Training Find a service provider Driver matrices (Most common files) Applicable countries and regions Select your product below: Products Value Line desktops Value Line notebooks Ethernet Adapters IBM PC ... ThinkVantage Technologies Note: Beginning August 2009, all 3000 family systems will be categorized as Value Line. For more information please click here Applicable countries and regions Worldwide Back to top Document id: DRVR-MATRIX Last modified: 2009-08-23 Document options Printable version Enter a product number Warranty Upgrade Lenovo Forums Virus Removal Service ... Subscribe to drivers updates Select your type ThinkPad ThinkCentre ThinkStation ThinkServer IdeaPad Essential Notebooks Essential Desktops Quick links Driver Matrices Personal Systems Reference (PSREF) Take our survey Printable version ... Contact

50. Rotation Matrix -- From Wolfram MathWorld Orthogonal matrices have special properties which allow them to be manipulated and identified with particular ease. Let and be two orthogonal matrices. http://mathworld.wolfram.com/RotationMatrix.html

51. NLinAlg - A .NET Class Library For Algebra Structures A .NET class library for working with algebra structures such as matrices and vectors. Open source, GPL http://nlinalg.sourceforge.net/

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52. The History Of Matrices The orgins of mathematical matrices lie with the study of systems of simultaneous linear equations. An important Chinese text from between 300 BC and AD 200 http://ualr.edu/lasmoller/matrices.html

Did you know . . .? The history of matrices goes back to ancient times! But the term "matrix" was not applied to the concept until 1850. "Matrix" is the Latin word for womb, and it retains that sense in English. It can also mean more generally any place in which something is formed or produced. The orgins of mathematical matrices lie with the study of systems of simultaneous linear equations. An important Chinese text from between 300 BC and AD 200, Nine Chapters of the Mathematical Art Chiu Chang Suan Shu ), gives the first known example of the use of matrix methods to solve simultaneous equations. In the treatise's seventh chapter, "Too much and not enough," the concept of a determinant first appears, nearly two millennia before its supposed invention by the Japanese mathematician Seki Kowa in 1683 or his German contemporary Gottfried Leibnitz (who is also credited with the invention of differential calculus, separately from but simultaneously with Isaac Newton). More uses of matrix-like arrangements of numbers appear in chapter eight, "Methods of rectangular arrays," in which a method is given for solving simultaneous equations using a counting board that is mathematically identical to the modern matrix method of solution outlined by

53. Linear Algebra/Matrices - Wikibooks, Collection Of Open-content Textbooks matrices and Linear Transformations. It turns out that linear transformations can be represented in a 11 fashion in matrices. This chapter will be most likely be a review as http://en.wikibooks.org/wiki/Linear_Algebra/Matrices

Linear Algebra/Matrices From Wikibooks, the open-content textbooks collection Linear Algebra This page may need to be reviewed for quality. Jump to: navigation search Contents Matrices and Linear Transformations Algebra of Transformations Addition Scalar multiplication ... edit Matrices and Linear Transformations It turns out that linear transformations can be represented in a 1-1 fashion in matrices. This chapter will be most likely be a review as the topic has already probably been covered in high school (see this link ). The establishment of a one-to-one correspondence between linear transformations and matrices is very important in the study of linear transformations. Suppose you have a set of basis vectors x , x , x , ..., x m of a vector space X and basis vectors y , y , y , ..., y n of a vector space Y. Consider a linear transformation T from X to Y, and the vectors T(x )=y a +y a +y a +...+y n a T(x )=y a +y a +y a +...+y n a T(x )=y a +y a +y a +...+y n a T(x m )=y a +y a +y a +...+y n a nm You can arrange these coefficients in a matrix Thus, if you have any vector Then Thus, T(x) is a linear combination of basis vectors

54. Matrix Workshop Manipulates matrices of both real and complex numbers. Win95/98/Me/NT/2000 http://business.fortunecity.com/interest/259/matrix.htm

55. EEOICP Site Exposure Matrices WebsiteHome Page US Department of Labor OWCP s mission is to enhance the welfare and protect the rights of American workers by enforcing employment laws. http://www.sem.dol.gov/

56. Matrix (mathematics) - Simple English Wikipedia, The Free Encyclopedia In mathematics, a matrix (plural matrices) is a rectangular table of numbers. There are rules for adding, subtracting and multiplying matrices together, but the rules are http://simple.wikipedia.org/wiki/Matrix_(mathematics)

Matrix (mathematics) From Wikipedia, the free encyclopedia Jump to: navigation search Specific entries of a matrix are often referenced by using pairs of subscripts. In mathematics , a matrix (plural matrices ) is a rectangular table of numbers . There are rules for adding subtracting and "multiplying" matrices together, but the rules are different than for numbers. As an example, does not always give the same result as , which is the case for the multiplication of ordinary numbers. Many natural sciences use matrices quite a lot. In many universities , courses about matrices (usually called linear algebra ) are taught very early, sometimes even in the first year of studies. Matrices are also very common in computer science Contents Definitions and notations Example Operations Addition ... change Definitions and notations The horizontal lines in a matrix are called rows and the vertical lines are called columns . A matrix with m rows and n columns is called an m -by- n matrix (or m n matrix) and m and n are called its dimensions The places in the matrix where the numbers are, are called

57. Atomatrix Multithreaded execution system of atomic matrices with dynamic compiler, a network environment, and an object-oriented OS. Open source, BSD. http://atomatrix.sourceforge.net/

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58. Ele-Math – Operators And Matrices: Submissions Operators and matrices ( OaM ) aims towards developing a high standard international journal which will publish top quality research and expository papers http://oam.ele-math.com/submission

OaM Volume 1 Volume 2 Volume 3 ... Ele-Math Home ABBREVIATION OaM, Oper. Matrices ISSN AIMS AND SCOPE Operators and Matrices OaM ') aims towards developing a high standard international journal which will publish top quality research and expository papers in matrix and operator theory and their applications. The journal will publish mainly pure mathematics, but occasionally papers of a more applied nature could be accepted. ' OaM ' will also publish relevant book reviews. OaM ' is published quarterly, in March, June, September and December. SUBMISSION SUBMISSION OF PAPERS Manuscripts should be submitted electronically in PostScript or Adobe Acrobat PDF format to the ' OaM ' Editorial Office through the provided web interface. The author who submitted the article for publication will be denoted as a corresponding author. He/She manages all communication and correspondence with the ' OaM ' regarding the article. Authors may indicate a member of the Editorial Board whom they consider appropriate for the article. However, assignment to that particular editor is not assured. In order to facilitate refereeing, copies of those papers (whether by the author or someone else) which are essential and referred to in the manuscript but are not conveniently accessible, should be enclosed.

59. Pauls Online Notes : Linear Algebra - Matrices You can navigate through this EBook using the menu to the left. For E-Books that have a Chapter/Section organization each option in the menu to the left indicates a chapter and http://tutorial.math.lamar.edu/Classes/LinAlg/Matrices.aspx

MPBodyInit('Matrices_files') Paul's Online Math Notes Online Notes / Linear Algebra / Systems of Equations and Matrices / Matrices Linear Algebra You can navigate through this E-Book using the menu to the left. For E-Books that have a Chapter/Section organization each option in the menu to the left indicates a chapter and will open a menu showing the sections in that chapter. Alternatively, you can navigate to the next/previous section or chapter by clicking the links in the boxes at the very top and bottom of the material. Also, depending upon the E-Book, it will be possible to download the complete E-Book, the chapter containing the current section and/or the current section. You can do this be clicking on the E-Book Chapter , and/or the Section link provided below. For those pages with mathematics on them you can, in most cases, enlarge the mathematics portion by clicking on the equation. Click the enlarged version to hide it. Solving Systems of Equations E-Book Chapter Section Matrices In the previous section we used augmented matrices to denote a system of linear equations.  In this section we’re going to start looking at matrices in more generality.  A matrix is nothing more than a rectangular array of numbers and each of the numbers in the matrix is called an

60. Hierarchical Matrices Hierarchical matrices are an efficient tool for the approximation of dense matrices resulting from the discretization of integral operators or partial http://www.hlib.org/

News Literature FAQs HLib HLib patches ... Contact Hierarchical Matrices News Bug in HLib: Incorrect quadrature for two-dimensional boundary elements The singular quadrature routines in used for discretizing integral operators in curvebem relied on invalid symmetry assumptions, and the logarithmic kernel function used in curvebem was treated incorrectly in the computation of the diagonal entries of the single layer potential matrix. Both problems are solved by a patch available at the HLib patches page Winterschool on hierarchical matrices. The next winterschool on hierarchical matrices will be part of the Haussdorf Center for Mathematics Trimester Program "Analysis and Numerics for high-dimensional problems" in July 2011. New Paper: Adaptive variable-rank approximation of general dense matrices. The paper introduces a modification of the standard H -matrix recompression algorithm presented in that allows it to reduce the storage requirements by using techniques introduced in the context of variable-order approximation schemes New paper: Data-sparse approximation of non-local operators by H -matrices.

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