81. Matrices Can Be Your Friends. matrices can be your Friends. This is a do nothing matrix. matrices are really easy it s just a matter of looking at them pictorially. http://www.sjbaker.org/steve/omniv/matrices_can_be_your_friends.html

Matrices can be your Friends. By Steve Baker What stops most novice graphics programmers from getting friendly with matrices is that they look like 16 utterly random numbers. However, a little mental picture that I have seems to help most people to make sense of what's going on. Most programmers are visual thinkers and don't take kindly to piles of abstract math. Take an OpenGL matrix: float m [ 16 ] ; Consider this as a 4x4 array with it's elements laid out into four columns like this: m[0] m[4] m[ 8] m[12] m[1] m[5] m[ 9] m[13] m[2] m[6] m[10] m[14] m[3] m[7] m[11] m[15] WARNING: Mathematicians like to see their matrices laid out on paper this way (with the array indices increasing down the columns instead of across the rows as a programmer would usually write them). Look CAREFULLY at the order of the matrix elements in the layout above! ...but we are OpenGL programmers - not mathematicians - right?! The reason OpenGL arrays are laid out in what some people would consider to be the opposite direction to mathematical convention is somewhat lost in the mists of time. However, it turns out to be a happy accident as we will see later. If you are dealing with a matrix which only deals with rigid bodies (ie no scale, shear, squash, etc) then the last row (array elements 3,7,11 and 15) are always 0,0,0 and 1 respectively and so long as they always maintain those values, we can safely forget about them for now.

82. JACAL An interactive symbolic mathematics program. JACAL can manipulate and simplify equations, scalars, vectors, and matrices of single and multiple valued algebraic expressions containing numbers, variables, radicals, and algebraic differential, and holonomic functions. Linux RPM distribution. http://swissnet.ai.mit.edu/~jaffer/JACAL.html

http://swiss.csail.mit.edu/~jaffer/JACAL JACAL Current Version Released Terms GPL JACAL is an interactive symbolic mathematics program. JACAL can manipulate and simplify equations, scalars, vectors, and matrices of single and multiple valued algebraic expressions containing numbers, variables, radicals, and algebraic differential, and holonomic functions. New: jacal script ported to Gambit. Quick Start Obtain jacal1b4.zip (240.kB) or jacal-1b4-1.noarch.rpm ; (210.kB) and install. Obtain slib3a1.zip (860.kB) and install. Obtain a Scheme implementation. The SCM Scheme Implementation compiles on a wide variety of platforms. To use SCM.EXE , a no-frills MS-DOS/Windows executable: Obtain scm.exe (265.kB) and scm5d9.zip (840.kB) and install. Documentation and Theory Online JACAL Manual; or jacal.pdf Algebra and the Lambda Calculus Solving Algebraic First Order Differential Equations (.pdf 90.kB), .dvi (12.kB) or .ps (90.kB) Algorithm to Remove Radicals From Denominators JACAL Development Plans for JACAL2 Savannah: CVS Repository jacal/jacal Development Snapshot jacal.zip

83. Teaching Resources, Rubrics, Matrices, Utilities Teaching Resources, Rubrics, matrices, Utilities. To other Duffy Pages. Teachers and Education. Pics4Learning, Secondary Assessment http://library.trinity.wa.edu.au/teaching/resources.htm

Trinity College Western Australia Teaching Resources, Rubrics, Matrices, Utilities To other Duffy Pages Teachers and Education Secondary Assessment Tools Baltimore Public Schools Performance Assessment Products Baltimore Public Schools Reading Focusing on Outcomes DET The Assessment Matrix - One Approach to Assessing Outcomes Jim Fuller Textmapping Project Reading Comprehension Writing Rubric Builder ClassWeb Tools David Warlick RubiStar Rubrics for project based activities Benefits of Textmapping Textmapping Project Web Graphics- Resources and Design Virtual Teacher Australia Question Builder ClassWeb Tools David Warlick Rubrics The Staff Room for Ontario Teachers Evaluating Web Sites Includes worksheets and rubrics to do this.

84. 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: 12 May 2004 There is now a mirror site , which will contain the same current versions as this site. There is also a page of FAQ , which I will add to as necessary. Generous Peanut users have established a mailing list , a database for sharing documents, and German and French versions of this page. Click the following links to reach the download pages: Wingeom (03 Apr 2004) Winplot (03 May 2004) Winstats (12 May 2004) Winarc (11 Apr 2004) Winfeed (26 Oct 2003) Windisc (27 Apr 2004) Winlab (07 Jul 2000) Winmat (03 Apr 2004) Wincalc (23 Feb 2004) Documents (4 Jun 2003) 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

85. Matrices And Other Arrays In LaTeX matrices and other arrays in LaTeX. matrices and other arrays are produced in LaTeX using the \textbf{array} environment. For example http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/Matrices.html

Matrices and other arrays in LaTeX This passage is produced by the following input: First of all, note the use of and to produce the large delimiters around the arrays. As we have already seen, if we use then the size of the parentheses is chosen to match the subformula that they enclose. Next note the use of the alignment tab character to separate the entries of the matrix and the use of to separate the rows of the matrix, exactly as in the construction of multiline formulae described above. We begin the array with and end it with . The only thing left to explain, therefore, is the mysterious which occurs immediately after . Now each of the c 's in represents a column of the matrix and indicates that the entries of the column should be centred. If the c were replaced by l then the corresponding column would be typeset with all the entries left-justified, and r would produce a column with all entries right-justified. Thus produces We can use the array environment to produce formulae such as Note that both columns of this array are set flush left. Thus we use immediately after . The large brace is produced using . However this requires a corresponding discussed earlier. This delimiter is invisible. We can therefore obtain the above formula by typing

86. Index Of /~ltw/hompack90 Suite of Fortran 90 subroutines by Layne T. Watson for solving nonlinear systems of equations by homotopy methods. There are subroutines for fixed point, zero finding, and general homotopy curve tracking problems, utilizing both dense and sparse Jacobian matrices, and implementing three different algorithms ODEbased, normal flow, and augmented Jacobian. http://people.cs.vt.edu/~ltw/hompack90/

Index of /~ltw/hompack90 Name Last modified Size Description ... Parent Directory 02-Jun-2004 11:30 - HOMPACK90.f 27-Mar-1997 13:25 389k INNHP.DAT 12-Sep-1996 09:34 1k LAPACK.f 12-Sep-1996 09:34 195k MAINF.f 04-Oct-1996 17:54 17k MAINF.out 03-Oct-1996 22:59 1k MAINP.f 04-Oct-1996 18:09 16k MAINP.out 04-Oct-1996 18:10 3k MAINS.f 12-Sep-1996 09:34 16k MAINS.out 12-Sep-1996 09:34 2k template.f 01-Mar-1997 10:22 6k

87. The Hadamard Maximal Determinant Problem List of known {1,1}-matrices with largest determinant and D-optimal designs. http://www.indiana.edu/~maxdet

The Hadamard maximal determinant problem The Hadamard maximal determinant problem asks when a matrix of a given order with entries -1 and +1 has the largest possible determinant. Despite well over a century of work by mathematicians, beginning with Sylvester's investigations of 1867, the question remains unanswered in general. The table lists current record determinants. Clicking on a determinant will display a maximal matrix or matrices and other relevant information including references to the literature. Table of maximal determinants, orders - 39 Det should be multiplied by 2 N-1 . Refer to key for more information. N Det R N Det R N Det R N Det R The aim of this page is to inspire people to try to improve the above numbers (where possible). If you are aware of better bounds or other constructions, please notify the authors of this page (email: maxdet at indiana dot edu). Likewise, if you feel your work, or somebody else's, is not properly credited, we want to hear from you! Related links: Roland Dowdeswell, Michael Neubauer, Bruce Solomon and Kagan Tumer set up an earlier web site on a similar theme. The site is connected to a continuously running search program. The current best lower bounds for orders 22, 23, 29, 31, 33, and 34 were discovered either by this program, or by Bruce Solomon using an improved version of the algorithm.

88. ASMs: Conference For Robbins' 60th Birthday ALTERNATING SIGN matrices A Conference in Honor of David P. Robbins June 2930, 2003. Location About a hundred mathematicians joined http://www.haverford.edu/math/lbutler/RobbinsConf.html

ALTERNATING SIGN MATRICES A Conference in Honor of David P. Robbins June 29-30, 2003 Location: About a hundred mathematicians joined us at the IDA Center for Communications Research in Princeton , where Dave Robbins has worked for 23 years. Our new building is at 805 Bunn Drive in Princeton, NJ. The closest airports are Newark and Philadelphia, each about an hour from Princeton. To get to CCR-P from US 1 near Princeton, take Harrison Street north. One mile after the intersection with Nassau Street in downtown Princeton, fork slightly right onto Bunn Drive. After three quarters of a mile, turn right into CCR-P. The conference opened on Sunday at 10:45 am and closed on Monday at noon. Talks: The speakers pitched their talks to mathematicians who are not experts on alternating sign matrices. For an introduction to alternating sign matrices, take a look at Dave Robbins's 1991 paper in the Mathematical Intelligencer, "The story of 1, 2, 7, 42, 429, 7436, ...", or David Bressoud's 1999 paper with Jim Propp in the Notices of the American Mathematical Society, "How the Alternating Sign Matrix Conjecture Was Solved" . The titles below are linked to the speakers' abstracts. REGRETFULLY CANCELLED Richard Stanley

89. Operaciones Con Matrices Translate this page Operaciones con matrices. Fecha de primera versión 22-09-01 Fecha de última actualización 10/11/2001. Suma. Producto de matrices. http://www.terra.es/personal/jftjft/Algebra/Matrices/OpeMat.htm

Operaciones con matrices Fecha de primera versión: 22-09-01 Fecha de última actualización: Suma Para sumar dos matrices tienen que tener las mismas dimensiones. Para sumar dos matrices se suman los elementos que ocupan las mismas posiciones Ejemplo: La suma de matrices tiene la propiedad conmutativa. A + B = B + A. Producto de un número por una matriz. Para multiplicar un numero por una matriz, se multiplica cada elemento de la matriz por el número. Ejemplo: -2 1 x 2 = -4 2 Producto de matrices Para multiplicar dos matrices es indispensable que el número de columnas de la primera matriz sea igual al número de filas de la segunda matriz. El producto de matrices no es conmutativo (no es lo mismo A.B que B.A). El producto de matrices tiene la propiedad asociativa : A . (B . C) = (A . B) . C Por ejemplo el producto de la matriz por la matriz es Si A y B tienen las dimensiones correctas para que se puedan multiplicar, entonces se cumple: (A.B)

90. Frontier Analytical Laboratory Specialist in trace level analysis of dioxin, furans and PCBs in various matrices by HR GCMS. Provides PDF chain of custody form, client login and contacts in El Dorado Hills, CA. http://www.frontieranalytical.com/

location.href='/external/index.stm'; We're sorry, you must have a Javascript enabled browser to view the rest of our website. Instructions on enabling Javascript in common browsers and more information about Frontier Analytical Laboratory is below. If you need futher assistance, please feel free to contact us. Contact Information 5172 Hillsdale Circle El Dorado Hills, CA 95762 916-934-0900 (FON) 916-934-0999 (FAX) info@frontieranalytical.com About Frontier Analytical Laboratory Frontier Analytical Laboratory is an analytical laboratory that specializes in the analysis of polychlorinated dibenzo dioxins and furans (PCDD/Fs), polychlorinated biphenyls (PCBs), and polyaromatic hydrocarbons (PAHs) on a variety of matrices. We offer analytical testing using a wide range of methodologies accepted by the USEPA, California Air Resources Board (CARB), and NCASI. We routinely meet or exceed all detection limits or reporting limits required by each analytical method. Frontier Analytical Laboratory, formed in 2001, is classified as a small business and is located in El Dorado Hills, California. Our laboratory is housed in a custom designed five thousand (5000) square foot building that enjoys a spacious instrument area containing two high-resolution mass spectrometers (with room for expansion). Our sample preparation and separate glassware areas are large and feature open floor plans. All facets of the laboratory were designed to promote quality, productivity, safety, and communication.

91. Calculator For Vectors, Matrices, Complex Number, Quaternion, Coordinates, Inter Calculator for vectors, matrices, complex numbers, coordinates, function plotting and intersections. Cartesian, spherical and cylindrical coordinates can be transformed into each other. Also integrated editor, arithmetic trainer, calendar, and help file. http://www.calc3d.com/

Mathematiksoftware Unterrichtssoftware The best math software since counting dry chicken bones (Windows 95/98/ NT/XP/ 2000). Now for the unbeatable cheap prize of only 16 USD !! The calculator can do statistics, best fits, function plotting, integration. It handles vectors matrices complex numbers quaternions ... regular polygons and intersections For point line, plane , sphere, circle Calc 3D calculates distances, intersections, and some additional information like volume and area. Cartesian, spherical and cylindrical coordinates can be transformed into each other. Carthesian plot, polar plot parametric plot best fit , fast fourier transformation, histogram, smooth,... Several languages can be handeled. Look at the overview of features Make a tour through Calc 3D Download Calc 3D Demos A short journey to Calc 3D Pro (A first and fast overview) Flash (1.5MB) Java (806.4KB) The other demos provide for different topics more details: Intersection of a line and a plane Flash (317.3KB) Java (60.4KB) Input of datavalues Flash (325.5KB)

92. Changing Shapes With Matrices 6. Changing Shapes With matrices ISBN 096216743-6; 80 pp.; 8 1/2x11 . He uses matrices to do these transformations and for us to simulate the plane s flight. http://www.shout.net/~mathman/html/matrices.html

6. "Changing Shapes With Matrices" ISBN 09621674-3-6; 80 pp.; 8 1/2x11" In his new book, Don shows how young people can do matrix transformations Valorie, age 11, made up a matrix that caused a change (or transformation) in the shape of a dog, similar to the one D'Arcy Thompson talked about with fish in his 1917 classic 'On Growth and Form' , also shown in the book 'The Art of Graphics for the IBM PC' written in 1986! Exciting stuff! Preface: Why transformations and why matrices? A Map to Transformations Chapter 1: Plotting points - graphing linear equations Chapter 2: Grocery store arithmetic to multiply matrices Chapter 3: Steps to do a transformation and a point-by-point restatement of Valerie's work Chapter 4: Questions and other student work Chapter 5: Some special matrices Appendix 1: Selected answers Appendix 2: Transformations without matrices Appendix 3: Graph paper to copy Appendix 4: Computer programs to do the transformations Appendix 5: Bibliography Appendix 6: The 81-2x2 matrices using only 1's, 0's or -1's, and their rules

93. Stamm – Estampación De Piezas Y Fabricación De Matrices, Stamm – Estampació Fabricantes y dise±adores de matrices, piezas estampadas mediante el uso de prensas hidr¡ulicas o mec¡nicas, y conjuntos soldados. http://www.stamm-sa.com/

Fabricantes y diseñadores de matrices, piezas estampadas (mediante el uso de prensas hidráulicas o mecánicas), y conjuntos soldados (con soldadura por puntos o por arco: TIG y MIG). Presentación Localización Secciones Calidad ... Contacte con nosotros Esta página utiliza frames, pero su navegador no los admite. En este momento usted está leyendo un resumen de nuestro sitio web

94. CEA/SPhT Ecole De Physique Des Houches 2004 Ecole de Physique des Houches Applications of Random matrices in Physics. June 625 2004. Marie Curie Training Course 6th Framework Program of the EU, NATO ASI. http://www-spht.cea.fr/pisp/serban/houches.html

CEA/SPhT : SERBAN-TEODORESCU Didina serban@spht.saclay.cea.fr Plan du site Applications of Random Matrices in Physics June 6-25 2004 Marie Curie Training Course 6th Framework Program of the EU NATO ASI Scientific direction: , ENS Paris Volodya Kazakov , ENS Paris Didina Serban , SPhT Saclay Paul Wiegmann , Enrico Fermi Institute, Chicago Anton Zabrodin , ITEP Moscow Scope of the school: Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories.

95. MATH-ASSISTANCE Lists rules and formulas for a number of mathematical subjects, such as plotting graphics, functions, factoring, derivatives, integrals, matrices, vectors, and numerical analysis. In English, French and Turkish languages. http://www.ercangurvit.com/

MATH ASSISTANCE ONLINE gurvit@ultratv.net FRANÇAIS ENGLISH TÜRKÇE Tracer des graphiques Geometrie analytique Nombres complexes Analyse complexe-I ... Dinamiðin Temel Prensibi s="na";c="na";j="na";f=""+escape(document.referrer) Mesure d'audience et statistiques Classement des meilleurs sites, chat, sondage Votez pour ce site au Weborama www.homepageclub.org

96. Mkaz.com : Java Matrix Calculator java MatrixCalculator. Screen Shot. Matrix Calculator Tips/Help. All matrices must be symmetric (nxn). Enter Matrix Elements Row by Row seperated by spaces. Ex. http://www.mkaz.com/math/matrix.html

Mathematics My Articles Snapshots Java Matrix Calculator Author: Marcus Kazmierczak Created On: Last Modified: June 13th, 2002 NOTE: The older Java Applet version of this program has been removed. I lost the complete source many computers ago. I have re-written the GUI as a Swing application, source code is fully available. Download the Java Source: MatrixCalculator.java Compile and Run Matrix Calculator No special classes or libraries are used with this application. The complete source resides in the one file above. After downloading, the following should work in any JDK 1.2 compatible compiler: $ javac MatrixCalculator.java $ java MatrixCalculator Screen Shot Matrix Calculator Tips/Help All Matrices must be symmetric (n x n) Enter Matrix Elements Row by Row seperated by spaces. Ex. (3x3) Results will be placed in the C matrix. The calculation of the determinant, by definition, is based upon a factorial number of calculations with respect to the size of the matrix. ie. a 3x3 matrix would have 6 calculations (3!) to make, whereas a 20x20 matrix would have 2.43 x 10^18 calculations (20!). So instead of brute forcing the calculations, I first do some operations on the matrix, which converts it to a upper triangular matrix, and then calculate the determinant by multipling down the diagonal, since everything below is 0, this will give the determinant. Floating Points and Accuracies For some reason computers aren't as accurate as I think they are, probably my calculation techniques. The accuracy of the numbers are probably only to 3 maybe 2 decimal places. If you keep applying operations to matrices and then use the resultant matrix a couple of times, the decimals get out of whack. Calculating an inverse and then multplying the matrix by it, is a good example of this.

97. DESCRIPTION OF CMAT A matrix calculator program, written in C. Calculations can be performed on matrices with complex rational coefficients using exact arithmetic routines, as well as on matrices with elements mod p. http://www.numbertheory.org/cmat/krm_cmat.html

CMAT CMAT is a matrix calculator program, written in C. Calculations can be performed on matrices with complex rational coefficients using exact arithmetic routines, as well as on matrices with elements mod p. There is also a DOS version which runs on 386/486+ machines. The DOS version, together with the C source, can be downloaded People using the UNIX version have to create a .cmatrc file in the working directory, consisting of the two lines datpath=. cmat=. (Also see cmat_bugfix.html for bug reports.) There are three calculator programs within CMAT: CMATR, CMATCR and CMATM. CMATR works over the rationals, CMATCR works the field of complex rationals and CMATM works over the field of p elements, where p is any prime less than 2 The programs use multiple precision arithmetic routines based on those in [ Fla ][342-357,175-185]. (See documentation Up to M0 (=30) objects of each type can be created and stored for use in future sessions. (rational) numbers: R[0],...,R[M0-1]; (rational) matrices: RM[0],...,RM[M0-1]; polynomials (rational): PR[0],...,PR[M0-1];

98. Arageli C++ template library for computations in ARithmetics, Algebra, GEometry, Linear and Integer linear programming. Supports arbitrary length integers, rationals, vectors, matrices. http://www.uic.nnov.ru/~zny/arageli/arageli.html

Arageli Arageli is the C++ library and the package of programs for computations in ar ithmetic, a lgebra, ge ometry, l inear and i nteger linear programming. Current version contains the implementation of arbitary precision arithmetic on integer and rational numbers (synonyms: multiple precision arithmetic, multiple precision numbers, arbitrary precision arithmetic, arbitrary precision numbers, big numbers). Some time-critical parts are written in assembler. You can use this assembler code or C++ code instead. If you'd like to use the library you can: Read (incomplete) documentation for version 2.0 beta (online) Download Arageli library 2.0 beta (with documentation) Read documentation for version 1.1.1 (online) Download Arageli library 1.1.1 (with documentation) Download Arageli library 1.1 (with documentation) Download Arageli library 1.0 (with documentation) If you'd like to use the package you can: Read description of some programs (in Russian) Download the package If you are interested in Pascal library for arbitary precision arithmetic you can also try my old BP 7.0 unlimited-precision arithmetic package my home page File translated from T E X by T T H , version 3.00

99. Graph Theory Lesson 7 Graph Theory Lessons. graphic graphic graphic Lesson7 Adjacency matrices. The graph. Look at the adjacency matrices of a few more graphs. http://www.utc.edu/~cpmawata/petersen/lesson7.htm

100. Fast Statistical Methods Page Fortran 90 and 77 codes by W.H. Press and G.B. Rybicki, for fast inversion matrices of an exponential form arising from autocorrelation functions of OrnsteinUhlenbeck processes. http://www.lanl.gov/DLDSTP/fast/

Keywords (for robots): time series statistical methods Wiener filter optimal filters filtering linear prediction interpolation covariance matrix correlation function structure function exponential decay inverse of tridiagonal matrix Gaussian random process fast method order N methods least squares fitting Gauss-Markov unbiased low-frequency red pink noise random walk fractal This page is maintained by George Rybicki ( rybicki@cfa.harvard.edu ) and Bill Press ( wpress@cfa.harvard.edu ), as a location for our links to the subject, and as a distribution point for our source code that implements so-called "fast" statistical methods. We define "fast" methods as being methods that seem to require the inversion of a matrix the size of the data set (typically the covariance matrix S+N ), an n workload but actually can be done, thanks to special assumptions or approximations, in order n workload We are interested in fast methods because they are applicable to very large data sets, and because they provide an efficient and well-controlled alternative to various inferior and ad-hoc procedures for the interpolation or fitting of noisy, incomplete data sets. Our Publications Our principal published work on this subject is in PRL

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