101. Matrix Definitions Lesson - I Defines matrices and basic matrix terms, illustrating these terms with worked solutions to typical homework exercises. Augmented matrices. http://www.purplemath.com/modules/matrices.htm

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

102. Moock Flash Player Inspector Offers analysis of dioxins and furans for monitoring effluents and other matrices, at the Research and Productivity Council in Fredericton, NB, Canada. http://www.dioxinlab.com/

103. Matrices As Linear Transformations Mathematical methods for Physical Sciences. matrices as linear transformations of the plane. matrices can be interpreted as linear transformations of the plane. 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.

104. Fórmulas Y Teoremas Compilado de la asignatura de matematicas y estadistica. Incluye derivadas, integrales, matrices y distribuciones de probabilidad. http://apuntes.togetherhost.com/mapa.html

105. Rendering Of Matrices With CSS matrices with CSS. It is desirable to find a method to display matrices by means of X(HT)ML and CSS. Currently no real matrices can http://www.markschenk.com/cssexp/matrices/matrix.html

Matrices with CSS It is desirable to find a method to display matrices by means of X(HT)ML and CSS. Currently no real matrices can be created due to limitations in borderstyles, but a close attempt is possible. What would be desirable? Ordening in columns (i.e. vectors) instead of rows such as tables, little markup and easy scalability. The below technique attempts to satisfy these requests. This page is also available as XML with similar layout, but much reduced markup, replacing divs and classes by custom tags. Examples The outer div with the borders is display:inline-table (to allow multiple matrices on one line), the vectors are display:inline-table (to allow multiple vectors in one matrix) and the cells are display:block (which will force the cells to show below each other). In this setup both the vectors and the cells are coloured. Individual styling is always possible of course. The next example uses transpose vectors to create rows. The rows are display:table and the cells are display:table-cell . It is to be solved for a vector. a b A difficulty here is the rows cannot easily be given a background-color, as possible with the vectors, because background-color won't apply.

106. Collapsed Adjacency Matrices, Character Tables And Ramanujan Graphs A database of character tables of endomorphism rings. http://www.math.rwth-aachen.de/~Ines.Hoehler/

Collapsed Adjacency Matrices, Character Tables and Ramanujan Graphs This is a database of character tables of endomorphism rings. Let G be a finite group, K a field and M a finite set on which G acts transitively. For a in M let M ,...,M r be the distinct orbits of G a , which have respective representatives a =a, a ,..., a r . Let E i i [k,l] be the collapsed adjacency matrix for the orbital digraph (M,E i ). Therefore A i is defined as the number of neighbours of a k in M l (see PrSoi for details). Let R denote the endomorphism ring End KG ,...,S k The entries of a column of the character table are the eigenvalues of the corresponding orbital digraph (see PrSoi for details). (see CePoTeTrVe for details). For rank up to 5 the collapsed adjacency matrices have been computed by Cheryl E. Praeger and Leonard H. Soicher (PrSoi) . Several matrices (also for larger rank cases) can be found in IvLiLuSaSoi , where numerous further references are given.) The following matrices originally have been published in: LLS : Fi with 2 .M Soi : Co with 2 .O IM : J with 2 .M Nor : M with 2.BM.

107. Matrices Help Relationships matrices Help Relationships. William A. McWorter Jr. matrices Help Relationships; matrices Help Relationships An Airline Problem. http://www.cut-the-knot.org/blue/relation.shtml

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

108. Polyx: The Polynomial Toolbox 2.0 - Polynomial Equations, Polynomial Matrices A package for polynomials, polynomial matrices and their application in systems, signals and control. commercial http://www.polyx.com/

Polyx Ltd. Product Info Sales Best Paper Award ... Student Version NEW The MathWorks, Inc. European Mirror Site Patches for Matlab 6.5 Release 13 now available!

109. Math.com Online Solvers Matrices Online Solvers matrices The matrices section of QuickMath allows you to perform arithmetic operations on matrices. Currently you http://www.math.com/students/solvers/matrices/matrices.htm

Home Teacher Parents Glossary ... Email this page to a friend Select Tool Calculators Converters Graphers Resources Cool Tools References Study Tips Wonders of Math Search Online Solvers Matrices The matrices section of QuickMath allows you to perform arithmetic operations on matrices. Currently you can add or subtract matrices, multiply two matrices, multiply a matrix by a scalar and raise a matrix to any power. What is a matrix? A matrix is a rectangular array of elements (usually called scalars), which are set out in rows and columns. They have many uses in mathematics, including the transformation of coordinates and the solution of linear systems of equations. Here is an example of a 2x3 matrix : Arithmetic The arithmetic suite of commands allows you to add or subtract matrices, carry out matrix multiplication and scalar multiplication and raise a matrix to any power. Matrices are added to and subtracted from one another element by element. For instance, when adding two matrices A and B, the element at row 1, column1 of A is added to the element at row 2, column 2 of B to give the element at row 1, column 1 of the answer. This is repeated for all elements in the matrices. Consequently, you can only add and subtract matrices which are the same size.

110. 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.

111. Library Of Hadamard Matrices matrices of Order 16. Marshall Hall s five inequivalent matrices (16H1 , 16H2 , 16H3 , 16H4 , 16H5 ). Noburo Ito s 60 inequivalent matrices of order 24. http://www.uow.edu.au/~jennie/hadamard.html

Matrices of Order 16 Marshall Hall's five inequivalent matrices ( Some Constructions for order 20 Three inequivalent matrices ( ). The first is Paley I Construction, the second and third are Tonchev iii and 1v. Noburo Ito's 60 inequivalent matrices of order 24 see "Neil Sloane 's Library List". Profiles of inequivalent matrices. Defining sets for inequivalent matrices. Kimura's 487 inequivalent matrices of order 28 see "Neil Sloane 's Library List" For GECP for some of Kimura's Hadamard matrices Gaussian Elimination with Complete Pivoting. Some Constructions for order 32 Sylvester Construction ( ), Paley I Construction ( ), Paley II Construction (P12, P13, P14, P15, P16, P17, P18, P19), Marshall Hall Difference Set Construction ( ), W D Wallis Inequivalent (Code 32G05, 32G06, 32G07, 32G08, 32G09, 32G10, 32G11, 32G12, 32G13, 32G14, 32G15). Also refer to "Neil Sloane's Library List" An Extended Library of Hadamard Matrices Some Constructions for order 36 Eleven matrices found by Vladimir Tonchev 179 Further Hadamard matrices of order 36 Bush-type Hadamard matrix of order 36 found by Zvonimir Janko Regular Hadamard matrices of order 36 found by Jennifer Seberry Updated 6th June, 2001. Please email questions or comments to

112. Pull-out Response Of Hooked Steel Fibers 'Concrete Science and Engineering' Vol. 1 (1999) comprises a research paper on the effect of mechanical clamping on the pullout response of hooked steel fibers embedded in cementitious matrices. PDF, 983 kB http://www.rilem.net/cse01.pdf

113. Toeplitz And Circulant Matrices Toeplitz and Circulant matrices. Toeplitz and Circulant Matices A Review , by RM Gray. A very old (1971, revised 1977, 1993, 1997 http://www-ee.stanford.edu/~gray/toeplitz.html

T oeplitz and Circulant Matrices Toeplitz and Circulant Matices: A Review , by R. M. Gray. A very old (1971, revised 1977, 1993, 1997, 1998, 2000, 2001, 2002.) but still occasionally useful tutorial on Toeplitz and circulant matrices. The file is in Adobe portable document format (pdf). Free readers can be downloaded from Adobe The most recent revision (August 2002) fixes several errors pointed out by Cynthia Pozun of ENST and incorporates several minor revisions that attempt to clarify arguments. An index has been added. Comments and corrections are welcome to rmgray@stanford.edu.

114. The Test Matrix Toolbox Contains a collection of test matrices, routines for visualizing matrices, and miscellaneous routines that provide useful additions to MATLAB's existing set of functions. http://www.ma.man.ac.uk/~higham/testmat.html

The Test Matrix Toolbox The Test Matrix Toolbox (last release, 1995) has been superseded by the The Matrix Computation Toolbox (first release, 2002). Most of the test matrices in Test Matrix Toolbox have been incorporated into MATLAB in the gallery function. The new toolbox incorporates some of the other routines in the Test Matrix Toolbox (in some cases renamed) and adds several new ones.

115. Software Of The MaSe-team In Fortran 90, by the MaSe (matrices Having Structure) Team of the University of Leuven. http://www.cs.kuleuven.ac.be/~marc/software/

Software produced by members of the MaSe-team Semiseparable matrices and the symmetric eigenvalue problem We refer the interested reader to the software corresponding to the PhD-thesis of Raf Vandebril. An implicit QR-algorithm to compute the eigensystem of symmetric semiseparable matrices The Matlab-files as a tarred-file Reference: R. Vandebril, M. Van Barel and N. Mastronardi, An implicit QR algorithm for semiseparable matrices to compute the eigendecomposition of symmetric matrices, Department of Computer Science, K.U.Leuven, Report TW ?, Leuven, Belgium, ? 2003. Solving diagonal-plus-semiseparable systems using a QR or a URV decomposition The Matlab-files as a zipped-file. Reference: E. Van Camp, N. Mastronardi, and M. Van Barel, Two fast algorithms for solving diagonal-plus-semiseparable linear systems , Instituto per le Applicazioni del Calcolo "M. Picone", Sez. Bari (Consiglio Nazionale delle Ricerche) 17/2002, August 2002. Reducing a symmetric matrix by orthogonal similarity transformations into a semiseparable matrix and the link with the Lanczos-Ritz values The Matlab-files as a zipped-file or as a tarred-file Reference M. Van Barel, R. Vandebril and N. Mastronardi

116. Vectors, Tensors And Matrices Vectors, tensors and matrices. Literature. The book 1 March 1943. There are hundreds of books on matrices; you can use any of them. If http://www.plmsc.psu.edu/~www/matsc597/vectors/

117. Journal Of Composites For Construction - ASCE Publications Deals with composite materials consisting of continuous synthetic fibers and matrices for use in civil engineering structures and subjected to the loading and environments of the infrastructure. http://www.pubs.asce.org/journals/cc.html

ASCE Publications Home Page ] [ Online Issues: Browse Search Document Store Subscription Information ... Exit Editor in Chief: Charles E. Bakis Pennsylvania State University, USA cbakis@psu.edu Frequency: Bimonthly Table of Contents - Current Issues The Journal of Composites for Construction publishes original research papers, review papers, and case studies dealing with the use of fiber-reinforced composite materials in construction. Of special interest are papers that bridge the gap between research in the mechanics and manufacturing science of composite materials and the analysis and design of large civil engineering structural systems and their construction processes. The journal publishes papers about composite materials consisting of continuous synthetic fibers and matrices for use in civil engineering structures and subjected to the loadings and environments of the infrastructure. The journal also publishes papers about composite materials used in conjunction with traditional construction materials such as steel, concrete, and timber, either as reinforcing members or in hybrid systems for both new construction and for repair and rehabilitation of existing structures. ISSN: 1090-0268 ASCE Journals Home Page ] [ Online Issues: Browse Search CEDB Search Help ... Exit

118. Peter M Neumann The Queen's College, University of Oxford. Varieties of groups; finite permutation groups; infinite permutation groups; design of grouptheoretic algorithms; soluble groups; quantitative topics in group theory; matrices over finite fields; miscellaneous questions in combinatorics, geometry and general group theory; history of group theory. Chairman of the UK Mathematics Trust. http://www.maths.ox.ac.uk/~neumann/

Dr Peter M Neumann Tel: 01865 279178 Fax: 01865 790819 Email: peter.neumann@queens.ox.ac.uk Personal details Research Recent publications Personal Fellow and Praelector in Mathematics at The Queen's College , since 1966 and Lecturer (CUF) in the University of Oxford since 1967; visiting lecturer or visiting professor at various times at various universities in many parts of the world. In Queen's I teach all branches of pure mathematics to undergraduates. For the University I lecture to undergraduates and graduate students on anything of interest to myself and, I hope, to them; I also supervise MSc and DPhil students in any area related to my own research. So far 30 students have completed doctorates under my supervision. For the three academic years October 1995 to September 1998 I was seconded half-time to Staff Development to help with University Teacher Training within Oxford. Other positions include: Chairman of the United Kingdom Mathematics Trust (UKMT) ; Vice-President of the British Society for History of Mathematics (BSHM) ; Editor of London Mathematical Society Monographs (published for the Society by OUP); editor of

119. Brain Matrices pumps, syringe pumps, restrainers, stopcocks, gloves, Latex, cotton, metal mesh, Nitrile, NDEX, Research Equipment, Braintree Scientific, Brain matrices. http://www.braintreesci.com/matrice.htm

Precision Brain Slicer Acrylic Matrices Ajustable Matrices Brain Matrices NEW Anodized Aluminum Brain Slicer Ideal for frozen tissues. Take advantage of the superlative heat transfer characteristics of aluminum to better preserve tissue structure during freezing. Place the fresh tissue in the slicer, freeze, and slice. Also suitable for non-cryogenic applications. Available in the following sizes: Model Animal Specifications Price BS-AL-505C Mouse 0.5 mm section Coronal BS-AL-505S Mouse 0.5 mm section Sagittal BS-AL-5000C Mouse 1 mm section Coronal BS-AL-5000S Mouse 1 mm section Sagittal BS-AL-605C Rat 0.5 mm section Coronal BS-AL-605S Rat 0.5 mm section Sagittal BS-AL-6000C Rat 1 mm section Coronal BS-AL-6000S Rat 1 mm section Sagittal Order S for sagittal style, and C for a coronal style Precision Brain Slicer Acrylic Matrices Anodized Aluminum Adjustable Matrices Precision Brain Slicer The precision Brain Matrice is designed to aid the basic research scientist in the free hand dissection of discrete regions of the rodent brain. It allows the investigator to slice either coronal or sagittal sections through the brain (including the olfactory bulbs) at intervals as small as 1mm. All brain matrices are identical high grade zinc to insure reproducible sections on a day to day, year to year basis. Applications Biochemical Pharmacology: The reproducible removal of small brain regions for biochemical analysis, such as determination of neuro-transmitter and metabolite concentrations. Individual brain areas may be either dissected or micropunched from the slices formed.

120. MATLAB Version Of The UF Sparse Matrix Collection Provide a simple method for downloading sparse test matrices from real applications into MATLAB. http://www.cise.ufl.edu/research/sparse/mat

Tim Davis , Assoc. Prof. Room E338 CSE Building P.O. Box 116120 University of Florida Gainesville, FL 32611-6120 phone (352) 392-1481, fax (352) 392-1220 email: davis AT cise.ufl.edu MATLAB version of the UF sparse matrix collection An easy MATLAB interface to the UF sparse matrix collection The UFsparse package provides a simple MATLAB interface to the UF sparse matrix collection. Typing Problem = UFget ('HB/arc130') for example, will get the matrix of that name from the UF sparse matrix collection, save it in a local directory on your own computer, and then load it into MATLAB. The second time you load the matrix, the previously downloaded copy is used instead. Typing UFget alone prints out a list of available matrices and their characteristics. The matrix format is described in the README file for the MATLAB-format version of the UF sparse matrix collection. Click here for the UF Sparse Matrix Collection in Harwell/Boeing format Click here for a list of all matrices in the collection and their attributes back to Tim Davis' home page back to the sparse matrix research page Directories of the MATLAB version of the UF sparse matrix collection: Click on a directory below. To download a matrix, right click a compressed (*.mat.gz) file and select "save as...".

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