21. 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://www.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

22. Science News Online - Ivars Peterson's MathLand - 6/14/97 Illustrated article explaining how contra dance patterns and rhythms are formed. http://www.sciencenews.org/sn_arc97/6_14_97/mathland.htm

June 14, 1997 Contra Dancing and Matrices The origins of contra dancing go back to colonial days, and its roots can be traced to English country dance. It's really a group rather than a couples effort, and it has elements that might remind you of traditional square dancing. Rhythm and pattern are the keys. What's striking, says Scanlon, is that a remarkably high percentage of its practitioners are highly educated, often involved in mathematics, computers, or engineering. "The appeal seems to lie in its being a kind of 'set dancing,' where one's position relative to others while tracing patterns on the dance floor is paramount," he says. "Timing is also crucial, as is the ability to rapidly carry out called instructions and do fraction math on the fly." Scanlon introduced both the mathematical and performance sides of contra dancing to attendees earlier this year at the 2nd Annual Recreational Mathematics Conference (see "Fun and Games in Nevada" The music for contra dancing is highly structured. Everything occurs in units of four. The band plays a tune for 16 beats, repeats the tune, then plays a new tune for 16 beats and repeats that. An eight-beat section is known as a call, during which each block of four dancers executes a called-out instruction. An entire dance is precisely 64 beats long. When the dancers line up in their groups of four to produce a long column down the floor extending away from the band, each square block consisting of two couples can be thought of as a matrix. Each dancer (element of the matrix) is in a specific position within the block. The called instructions correspond to rearrangements of the elements of the matrix. After 64 beats, however, the first and second rows of the matrix must be interchanged. Of course, that can be done in one step, but the fun comes in all the different ways in which groups of four can get to that inevitable end result.

23. Toeplitz And Circulant Matrices A very old (1971, revised 1977, 1993, 1997, 1998, 2000, 2001, 2002, 2005, 2006) but still occasionally useful tutorial on Toeplitz and circulant matrices. http://www-ee.stanford.edu/~gray/toeplitz.html

T oeplitz and Circulant Matrices Toeplitz and Circulant Matrices: A Review , by R. M. Gray. A very old (1971, revised 1977, 1993, 1997, 1998, 2000, 2001, 2002, 2005, 2006) but still occasionally useful tutorial on Toeplitz and circulant matrices. The report was revised with the help of two very thorough reviewers and is being published both online and as a paperback book by NOW publishers. The official citation to the published version is R. M. Gray, "Toeplitz and Circulant Matrices: A review" Foundations and Trends in Communications and Information Theory, Vol 2, Issue 3, pp 155-239, 2006. Journal reprint Note: The typos found and noted below are corrected in the first pdf, but not in the second. A printed and bound version of the paperback book is available at a 35% discount from Now Publishers. This can be obtained by entering the promotional code on the order form at now publishers. You will then pay only $28.00 including postage. (The Website is due to be activated as soon as the book is available.) Typographical errors: On p. (62) the explanation of (5.1) is garbled. It published latex is

24. Raven Standard Progressive Matrices The Standard Progressive matrices (SPM) was designed to measure a person’s ability to form perceptual relations and to reason by analogy...... http://www.cps.nova.edu/~cpphelp/RSPM.html

Raven Standard Progressive Matrices Purpose: Designed to measure a person’s ability to form perceptual relations. Population: Ages 6 to adult. Score: Percentile ranks. Time: (45) minutes. Author: J.C. Raven. Publisher: U.S. Distributor: The Psychological Corporation. Description: The Standard Progressive Matrices (SPM) was designed to measure a person’s ability to form perceptual relations and to reason by analogy independent of language and formal schooling, and may be used with persons ranging in age from 6 years to adult. It is the first and most widely used of three instruments known as the Raven's Progressive Matrices, the other two being the Coloured Progressive Matrices (CPM) and the Advanced Progressive Matrices (APM). All three tests are measures of Spearman's g. Scoring: Reliability: Internal consistency studies using either the split-half method corrected for length or KR20 estimates result in values ranging from .60 to .98, with a median of .90. Test-retest correlations range from a low of .46 for an eleven-year interval to a high of .97 for a two-day interval. The median test-retest value is approximately .82. Coefficients close to this median value have been obtained with time intervals of a week to several weeks, with longer intervals associated with smaller values. Raven provided test-retest coefficients for several age groups: .88 (13 yrs. plus), .93 (under 30 yrs.), .88 (30-39 yrs.), .87 (40-49 yrs.), .83 (50 yrs. and over). Validity: Spearman considered the SPM to be the best measure of g. When evaluated by factor analytic methods which were used to define g initially, the SPM comes as close to measuring it as one might expect. The majority of studies which have factor analyzed the SPM along with other cognitive measures in Western cultures report loadings higher than .75 on a general factor. Concurrent validity coefficients between the SPM and the Stanford-Binet and Weschler scales range between .54 and .88, with the majority in the .70s and .80s.

25. EBI Help: Matrices This can then be used to produce tables(scoring matrices) of the relative frequencies with which amino acids replace each other over a short evolutionary http://www.ebi.ac.uk/help/matrix_frame.html

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26. Random Matrices Conference Call (617) 5770200, ask for reservations and tell them you are attending the Random matrices Conference. If you have trouble with reservations, call http://www-math.mit.edu/conferences/random/

Random Matrices Conference Sunday, August 12 th Schedule of titles and abstracts New applications of random matrix theory are popping up at a large rate these days. Nonetheless, the best engineering applications still are waiting to be found. This informal conference is a hope at bringing people together to explore these applications. The invited speakers include: Ioana Dumitriu (MIT) Partha Mitra (Bell Labs) David R. Nelson (Harvard) David Tse (Berkeley) Divikar Viswanath (U Chicago) See Schedule for titles and abstracts Lectures will take place at M.I.T. from 9:30am to 5:30pm in room 1-390. This map shows where Building 1 is and shows in what corner Room 390 can be found. Room 390 is on the third floor. If you would like a hotel reservation, please contact the University Park Hotel@MIT where a block of rooms has been reserved for Saturday and Sunday evenings at a special rate of $149 per night. Call (617) 577-0200, ask for "reservations" and tell them you are attending the "Random Matrices Conference." If you have trouble with "reservations," call Geoffrey Taylor in Sales at (617) 551-0312. Organizer: Alan Edelman (MIT) In cooperation with

27. 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 Winterschool on hierarchical matrices. The next winterschool on hierarchical matrices will take place at the Max Planck Institute for Mathematics in the Sciences from the 17th to the 20th of March, 2008. The deadline for registrations is the 31st of January, 2008. The winterschool will focus on the theoretical foundation of hierarchical matrix techniques and on the practical implementation of the corresponding algorithms and data structures in the context of the HLib package. Details can be found on the winterschool homepage 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. Although any matrix can be approximated by an H -matrix, the resulting rank may turn out to be too large for an efficient data-sparse representation. The paper

28. Weight Matrices For Sequence Similarity Scoring When we consider scoring matrices, we encounter the convention that matrices have numeric indices corresponding to the rows and columns of the matrix. http://www.techfak.uni-bielefeld.de/bcd/Curric/PrwAli/nodeD.html

Weight Matrices for Sequence Similarity Scoring Version 2.0 May 1996 David Wheeler , Ph.D. Department of Cell Biology, Baylor College of Medicine Houston, Texas E-mail: wheeler@bcm.tmc.edu Table of Contents Weight matrices for sequence similarity scoring Importance of scoring matrices Examples of matrices Log odds matrices ... Other specialized scoring matrices Weight Matrices for Sequence Similarity Scoring Outline: Objective: Overview of methods and theories that underlie the construction of scoring matrices. Examples of weight matrices for nucleotide and amino acid scoring. Transition probability matrix: PAM Construction Properties Sources of error BLOSUM matrix Construction Sources of error Practical aspects Other refinements to transition probability matrices. Reading: D.G. George, W. C. Barker and L. T. Hunt. (1990). Mutation Data Matrix and Its Uses. in Methods in Enzymology vol 183; R.F. Doolittle, ed. pp. 333-351. Academic Press, Inc. New York. M.O. Dayhoff (1978) Atlas of Protein Sequence and Structure (Natl. Biomed. Res. Found., Washington), Vol. 5, Suppl. 3, pp. 345-352. S.F. Altschul (1991). Amino acid substitution matrices from an information theoretic perspective. J. Mol. Biol. 219 555-565.

29. 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).

30. John Halleck's Matrices matrices of the same size may be added, by making a new matrix of the same size, with elements that just add the corresponding elements from the matrices http://home.utah.edu/~nahaj/math/matrices.html

Matrices I give up. I'm forced into a matrix review page. Grammarian note: It is one Matrix, two matrices. So... Here is a quick review Numbers Rows Columns Operations on rows and columns ... Positive Definite I have made a collection of Matrix Identities that I use. Reading them could be helpful in following the otherwise short derivations scattered around this paper. Numbers A single number in matrix notation is called a scalar . It can be looked at as a number, or as a 1 x 1 matrix, or as a one element row or column. Rows A row (also called a row vector) is just an ordered collection of elements. For example, [ a b c ] is a row. If you have two rows of the same length, you can add the rows by adding the corresponding elements in each row. For example, the row [ d e f ] + [ g h i ] = [ d+g e+h f+i ] One can multiply a row by a scalar (number). For example, 2 * [ a b c ] = [ 2a 2b 2c ] A row may have any number of elements, from one on up. If Z is a row, Z(i) means the i'th element of that row. Columns A column (also called a column vector) is just like a row, except it is arranged vertically. For example:

31. Luminy Conference On Random Matrices Luminy conference on random matrices. October 30 November 3, 2006 Organizers A. Kuijlaars and M. Ledoux. Theme of Conference http://wis.kuleuven.be/analyse/arno/luminy/index.html

Luminy conference on random matrices Home Travel information Program Contact Luminy conference on random matrices October 30 - November 3, 2006 Organizers: A. Kuijlaars and M. Ledoux Theme of Conference Random matrix theory has its origins in the 1920s in the works of Wishart in mathematical statistics and in the 1950s in the works of Wigner, Dyson and Mehta on the spectra of highly excited nuclei. Since then the subject has developed fast and has found applications in many branches of mathematics and physics, ranging from quantum field theory to statistical mechanics, integrable systems, number theory, statistics, and probability. The workshop intends to cover the recent advances in random matrix theory, with an emphasis on the probabilistic aspects. Location and Cost The conference will take place at the Centre International de Recherches Mathématiques ( CIRM ), Luminy, France. Accommodation and meals are provided for the participants for this period, at no cost. We are unable to provide any funding for travel. Confirmed participants G. Akemann (

32. SAMSI Program On High Dimensional Inference And Random Matrices The aim of the Program is to bring together researchers interested in the theory and applications of random matrices to share their results, http://www.samsi.info/programs/2006ranmatprogram.shtml

19 T.W. Alexander Drive P.O. Box 14006 Research Triangle Park, NC 27709-4006 Tel: 919.685.9350 Fax: 919.685.9360 info@samsi.info Programs Propose a Program Visitor Info 2006-07 Program on High Dimensional Inference and Random Matrices Research Foci Description of Activities Opening Workshop, Sept. 17-20, 2006 Working Groups ... Further Information RANDOM MATRIX THEORY lies at the confluence of several areas of mathematics, especially number theory, combinatorics, dynamical systems, diffusion processes, probability and statistics. At the same time Random Matrix Theory may hold the key to solving critical problems for a broad range of complex systems from biophysics to quantum chaos to signals and communication theory to machine learning to finance to geoscience modeling. This semester-long Program is a unique opportunity to explore the interplay of stochastic and mathematical aspects to random matrix theory and application. Program Leaders: Iain Johnstone (Stanford University, Chair), Peter Bickel (UC Berkeley), Helene Massam (York University), Douglas Nychka (NCAR), Craig Tracy (UC Davis); G. W. Stewart (Univ. of Maryland, National Advisory Committee Liaison), Chris Jones (SAMSI, Directorate Liaison) Scientific Committee: Myles Allen (Oxford), Estelle Basor (California Polytechnic, San Luis Obispo), David Donoho (Statistics, Stanford), Persi Diaconis (Statistics, Stanford), Jianqing Fan (Princeton), Ken McLaughlin (Mathematics, Univ. of Arizona), Neil O'Connell (Univ. of Warwick, UK), Ben Santner (Lawrence Livermore), Jack Silverstein (Mathematics, N.C. State), Ofer Zeitouni (Univ. of Minnesota)

33. Examples Of Intelligence Tests The Raven Progressive matrices test is a widely used intelligence test in many research and applied settings. In each test item, one is asked to find the http://wilderdom.com/intelligence/IQExampleTests.html

Individual Differences Understanding IQ Examples of Intelligence Tests Last updated: 20 Dec 2003 Example: Non verbal test - Raven's Progressive Matrices The Raven Progressive Matrices test is a widely used intelligence test in many research and applied settings. In each test item, one is asked to find the missing pattern in a series. Each set of items gets progressively harder, requiring greater cognitive capacity to encode and analyze. Sample item from the Raven Progressive Matrices tests Raven's Progressive Matrices was designed primarily as a measure of Spearman's g. There are no time limits and simple oral instructions. There are 3 different tests for different abilities: Coloured Progressed Matrices (younger children and special groups) Stanford Progressive Matrices (average 6 to 80 year olds) In terms of its psychometrics, Raven's Progressive Matrices: has good test-retest reliability between .70 and .90 (however, for low score ranges, the test-retest reliability is lower) has good internal consistency coefficients - mostly in the .80s and .90s

34. ONLamp.com -- Transformation Matrices Use transformation matrices to manipulate graphics. Examples given using Numerical Python and Dislin. http://www.onlamp.com/pub/a/python/2000/07/05/numerically.html

Sign In/My Account View Cart Articles Weblogs ... MySQL Conference and Expo April 14-17, 2008, Santa Clara, CA Listen Print Subscribe to Python Subscribe to Newsletters Transformation Matrices This month we'll use NumPy and DISLIN to create, display, and manipulate a basic geometric image. At the heart of image manipulation are special matrices that can be used to create effects. You can use these effects separately or combine them for more complex operations. While the focus is on two-dimensional operations, the concepts extend to three (and more) dimensions. They are fundamental to many applications including computer games and computer-aided design (CAD) programs. They are the heart of linear algebra itself. So what's a vector? Considering the world as a flat plane, we can lay on it two reference directions. The arrows labeled x and y provide a reference for our vector The vector is defined as being four units in the x direction and 3 units in the y direction (units, in this case, being miles traveled.) So how do we get from the motion of a car to a vector of ? Well we would say that the velocity of the car is miles per hour. Which means that the car moved four miles in the

35. Matriz (matemática) - Wikipedia, La Enciclopedia Libre Translate this page Dadas las matrices m-por-n A y B, su suma A + B es la matriz m-por-n calculada El producto de dos matrices no es conmutativo, es decir, AB BA. http://es.wikipedia.org/wiki/Matriz_(matemática)

Matriz (matem¡tica) De Wikipedia, la enciclopedia libre Saltar a navegaci³n bºsqueda En matem¡ticas , una matriz es una ordenaci³n rectangular de nºmeros , o m¡s generalmente, una tabla consistente en cantidades abstractas que pueden sumarse y multiplicarse Tabla de contenidos Definiciones y notaciones Ejemplo Suma de matrices Propiedades de la suma de matrices ... editar Definiciones y notaciones Una matriz es una tabla o arreglo rectangular de numeros. Los numeros en el arreglo se denominan elementos de la matriz. Las l­neas horizontales en una matriz se denominan filas y las l­neas verticales se denominan columnas . A una matriz con m filas y n columnas se le denomina matriz m -por- n (escrito m n ), y m y n son sus dimensiones . Las dimensiones de una matriz siempre se dan con el nºmero de filas primero y el nºmero de columnas despu©s. La entrada de una matriz A que se encuentra en la fila i -©sima y la columna j -©sima se le llama entrada i,j o entrada ( i j )-i©sima de A . Esto se escribe como A i,j o A i,j Normalmente se escribe para definir una matriz A m n con cada entrada en la matriz A i,j

36. HomePage There will be approximately 30 talks of 45 minutes length each, from the areas of integrable systems, random matrices, spectral theory, probability and http://math.arizona.edu/~mcl/ISRMA.html

Home Page Accommodations Program Registration ... Transportation Integrable Systems, Random Matrices, and Applications Courant Institute of Mathematical Sciences New York University New York, NY May 22 - 26, 2006 Support by the American Institute of Mathematics, the Courant Institute of Mathematical Sciences, and the National Science Foundation The Courant Institute is at 251 Mercer Street in Manhattan between 4th and 3rd Streets. DATES, TIMES, AND LOCATION The conference will be held at the Courant Institute of Mathematical Sciences of New York University from May 22 through May 26 of 2006. The talks will take place at the Courant Institute , which is located at 251 Mercer Street (corner of Mercer Street and West 4th Street) in Manhattan. ORGANIZING COMMITTEE Jinho Baik, Thomas Kriecherbauer, Luen-Chau Li, Ken McLaughlin Peter Sarnak , Carlos Tomei, and Xin Zhou If you have any question, please feel free to contact us. SPEAKERS Mark Ablowitz, UC Boulder: Integrable Systems: Painlev'e - Chazy - Ramanujan Michael Aizenman, Princeton: Green function fluctuations and spectral properties of random operators Eitan Bachmat

37. Mathematics Support For Engineering Students - Mathcentre matrices Mechanics Sequences Series Trigonometry Vectors « choose subject. matrices. Determinants Matrix arithmetic Solution of equations. http://www.mathcentre.ac.uk/students.php/engineering/matrices/

Students Engineering Students Staff Search News ... Contact Us Engineering Select a topic.. Algebra Arithmetic Complex Numbers Differentiation ... Vectors Matrices Determinants Matrix arithmetic Solution of equations

38. DIMACS Workshop On Random Matrices DIMACS Workshop on Random matrices. March 17 19, 2008 DIMACS Center, CoRE Building, Rutgers University. Organizer Van Vu, Rutgers University, http://dimacs.rutgers.edu/Workshops/RandomMatrices/

DIMACS Workshop on Random Matrices March 17 - 19, 2008 DIMACS Center, CoRE Building, Rutgers University Organizer: Van Vu , Rutgers University, vanvu at math.rutgers.edu Presented under the auspices of the Special Focus on Discrete Random Systems Workshop Announcement Call for Participation Program ... Application for Financial Support Limited financial support is expected to be available for students to attend the workshop. How much we offer will depend on funds we raise for this purpose and on the number of applications received and might have to be limited to waiver of registration fees for some of the students. Deadline for Applications: February 18, 2008 Registration Form (Pre-registration deadline: March 10, 2008) DIMACS Workshop Registration Fees Pre-register before deadline After pre-registration deadline Academic/nonprofit rate* (1 day/2 days/3 days) Regular rate (1 day/2 days/3 days) Postdocs $10/day $15/day DIMACS Postdocs $10/day $15/day DIMACS members and DIMACS partner institution employees** DIMACS long-term visitors*** * Registration fee to be collected on site, cash, check (payable to Rutgers University), VISA/Mastercard accepted.

39. Famous Matrices - Untitled It can be derived more directly via the theory of Cauchy matrices see J. W. Demmel, Applied Numerical Linear Algebra, page 92. http://www.gnu.org/software/octave/doc/interpreter/Famous-Matrices.html

Previous: Special Utility Matrices , Up: Matrix Manipulation 17.5 Famous Matrices The following functions return famous matrix forms. hadamard n Construct a Hadamard matrix Hn of size n -by- n . The size n must be of the form k p in which p is one of 1, 12, 20 or 28. The returned matrix is normalized, meaning Hn(:,1) == 1 and H(1,:) == 1 Some of the properties of Hadamard matrices are: kron ( Hm Hn is a Hadamard matrix of size m -by- n Hn * Hn' == n * eye ( n The rows of Hn are orthogonal. det ( A Hn for all A with abs ( A i j Multiply any row or column by -1 and still have a Hadamard matrix. hankel c, r Return the Hankel matrix constructed given the first column c , and (optionally) the last row r . If the last element of c is not the same as the first element of r , the last element of c is used. If the second argument is omitted, it is assumed to be a vector of zeros with the same size as c A Hankel matrix formed from an m-vector c , and an n-vector r , has the elements See also: vander, sylvester_matrix, hilb, invhilb, toeplitz. hilb n Return the Hilbert matrix of order n . The i, j element of a Hilbert matrix is defined as

40. Matrix Programming Guide For Cocoa: Introduction To Matrices Introduction to matrices. Contents. Organization of This Document “About matrices” provides basic information about matrices http://developer.apple.com/documentation/Cocoa/Conceptual/Matrix/Matrix.html

This document set is best viewed in a browser that supports iFrames. Advanced Search Log In Not a Member? Contact ADC ... Hide TOC Introduction to Matrices Contents: Organization of This Document See Also NSMatrix is a class used for creating groups of NSCells that work together in various ways. Organization of This Document This programming topic contains the following articles: provides basic information about matrices describes how the cells in a matrix behave when the matrix is tracking the mouse. discusses how to add and remove cells programatically. discusses how to change the appearance of a matrix and its cells. See Also If you want to group several elements visually, see the Boxes programming topic. Hide TOC Last updated: 2006-11-07 Did this document help you? Yes : Tell us what works for you. Report typos, inaccuracies, and so forth. : Tell us what would have helped. Get information on Apple products. Visit the Apple Store online or at retail locations. 1-800-MY-APPLE Privacy Notice

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