61. Multiplication Of Matrices Multiplication of matrices. Before we give the formal definition of how to multiply two matrices, we will discuss an example from a real life situation. http://www.sosmath.com/matrix/matrix1/matrix1.html

Multiplication of Matrices Before we give the formal definition of how to multiply two matrices, we will discuss an example from a real life situation. Consider a city with two kinds of population: the inner city population and the suburb population. We assume that every year 40% of the inner city population moves to the suburbs, while 30% of the suburb population moves to the inner part of the city. Let I (resp. S ) be the initial population of the inner city (resp. the suburban area). So after one year, the population of the inner part is I S while the population of the suburbs is I S After two years, the population of the inner city is I S I S and the suburban population is given by I S I S Is there a nice way of representing the two populations after a certain number of years? Let us show how matrices may be helpful to answer this question. Let us represent the two populations in one table (meaning a column object with two entries): So after one year the table which gives the two populations is If we consider the following rule ( the product of two matrices then the populations after one year are given by the formula After two years the populations are Combining this formula with the above result, we get

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

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

63. Determinant And Inverse Of Matrices Determinant and Inverse of matrices. Finding the inverse of a matrix is very important in many areas of science. For example, decrypting http://www.sosmath.com/matrix/inverse/inverse.html

Determinant and Inverse of Matrices Finding the inverse of a matrix is very important in many areas of science. For example, decrypting a coded message uses the inverse of a matrix. Determinant may be used to answer this problem. Indeed, let A be a square matrix. We know that A is invertible if and only if . Also if A has order n, then the cofactor A i j is defined as the determinant of the square matrix of order (n-1) obtained from A by removing the row number i and the column number j multiplied by i j . Recall for any fixed i , and for any fixed j . Define the adjoint of A , denoted adj A ), to be the transpose of the matrix whose ij th entry is A ij Example. Let We have Let us evaluate . We have Note that . Therefore, we have Is this formula only true for this matrix, or does a similar formula exist for any square matrix? In fact, we do have a similar formula. Theorem. For any square matrix A of order n, we have In particular, if , then For a square matrix of order 2, we have which gives This is a formula which we used on a previous page. On the next page, we will discuss the application of the above formulas to linear systems.

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

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

65. Mathematics Reference: Rules For Matrices Mathematics reference Rules for matrices, 18 Ma 8 MathRef. Basic properties of matrices. Legend. A, B, and C are matrices,; O http://www.alcyone.com/max/reference/maths/matrices.html

Mathematics reference Rules for matrices Ma MathRef Basic properties of matrices. Legend. A, B, and C are matrices, O represents the zero matrix, I represents the identity matrix, r s , and n are scalars. Basic. -A == (-1) A equation 1 A - B == A + (-B) equation 2 1 A = A equation 3 A = O equation 4 A + O = O + A = A equation 5 I A = A I = A equation 6 A - A = O equation 7 Addition and scalar product. A + B = B + A equation 8 (A + B) + C = A + (B + C) equation 9 r (A + B) = r A + r B equation 10 r s ) A = r A + s A equation 11 r s ) A = r s A) equation 12 Matrix product. A == I equation 13 A == A A equation 14 A n = A A n equation 15 (A B) C = A (B C) equation 16 A (B + C) = A B + A C equation 17 (A + B) C = A C + B C equation 18 Transpose and inverse. I T = I equation 19 (A T T = A equation 20 (A + B) T = A T + B T equation 21 r A) T r A T equation 22 (A B) T = B T A T equation 23 I = I equation 24 A A = A A = I equation 25 (A B) = B A equation 26 (A T = (A T equation 27 Trace. tr (A + B) = tr A + tr B equation 28 tr ( r A) = r tr A equation 29 tr (A B) = tr (B A) equation 30 Determinant and adjoint.

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

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67. The Matrix Market Matrices By Name matrices by Name. Use this list if you already know the name of the matrix you want; otherwise, go to Search. 1138 BUS 494 BUS 662 http://math.nist.gov/MatrixMarket/matrices.html

Matrices by Name Use this list if you already know the name of the matrix you want; otherwise, go to Search 1138 BUS 494 BUS 662 BUS ... ZENIOS The Matrix Market is a service of the Mathematical and Computational Sciences Division Information Technology Laboratory National Institute of Standards and Technology Home ... Resources Last change in this page: Tue May 14 17:10:06 US/Eastern 2002 [Comments: matrixmarket nist.gov

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

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

69. 12th International Workshop On Matrices And Statistics The 12th International Workshop on matrices and Statistics (IWMS2003) will be held at the University of Dortmund (Dortmund, Germany) on August 5-8. http://www.statistik.uni-dortmund.de/IWMS/main.html

Purpose and Location Connexions Organizing Committees Previous Workshops ... Workshop Programme Final Registration Paper Submission Accomodation th International Workshop on Matrices and Statistics IWMS-2003 Dortmund, Germany, August 5-8, 2003 home th International Workshop on Matrices and Statistics IWMS 2003 Purpose and Location The 12th International Workshop on Matrices and Statistics (IWMS-2003) will be held at the University of Dortmund (Dortmund, Germany) on August 5-8, 2003 with the purpose to foster the interaction of researchers in the interface between statistics and matrix theory. Organizing Committees How to reach Dortmund University? From Dortmund Central Station Dortmund University You can find a map of the university (in german) under layout of the university The workshop will take place in Building 13. Workshop Programme The Workshop Programme can be found here Previous Workshops This Workshop in Germany will be the 12th in a series. The 11th International Workshop on Matrices and Statistics was held at the Danish Technical University in Lyngby, Denmark: 29-31 August 2002. Forthcoming Workshop The 13th International Workshop on Matrices and Statistics (IWMS-2004) in celebration of I. Olkin's 80th birthday will be held in the Bedlewo, about 30 km. (20 miles) south of Poznan, Poland, from 19 to 21 August 2004.

70. Paper: Linear Codes By P. R. J. –sterg¥rd. The following codes with minimum distance greater than or equal to 3 are classified binary codes up to length 14, ternary codes up to length 11, and quaternary codes up to length 10. http://www.tcs.hut.fi/~pat/matrices.html

Classifying subspaces of Hamming spaces Designs, Codes and Cryptography The codes classified in the paper can here be obtained electronically. The following codes with minimum distance greater than or equal to 3 are classified: binary codes up to length 14, ternary codes up to length 11, and quaternary codes up to length 10. The parity check matrices of the codes are given, with the identity matrix part omitted. The first three lines of the files contain, respectively, the number of codes, the value of k (the dimension), and the value of r (the codimension). Then the parity check matrices are listed one by one using k rows of length r . To get an r x n parity check matrix, transpose these rows and add the r columns of the identity matrix. For the binary and ternary codes, the field elements are the integers modulo q a a a is a primitive element. An [ n k d ] code is a code with length n , dimension k , and minimum distance at least d . Please note that in the definition of equivalence for quaternary codes, we allow global conjugacy in addition to monomial transformations. (So there are here fewer inequivalent quaternary codes than in other published studies that use only monomial transformations.) Binary codes [3,1,3]: 1 codes

71. Matrices Of Performance Indicators matrices of Performance Indicators. These matrices are the results of a comparative review of a number of key documents on performance indicators for libraries. http://www.dmu.ac.uk/~camile/matrices/intro.htm

Matrices of Performance Indicators Introduction - Index to Matrices CAMILE Home Page Introduction These matrices are the results of a comparative review of a number of key documents on performance indicators for libraries. The review was commissioned by the DECIDE project and carried out by John Sumsion The matrices present a list of the performance indicators appearing in the following manuals (follow the links for more details): Moore, N. Measuring the Performance of Public Libraries: a Draft Manual . Paris, General Information Programme and UNISIST, UNESCO, January 1989. More details. Van House, Nancy A;Lynch, Mary Jo; McClure, Charles R; Zweizig, Douglas L;Rodger, Eleanor Jo. Output Measures for Public Libraries: A Manual of Standardized Procedures . Second edition. Chicago, American Library Association, 1987. More details. International Standards Organisation ISO 11620 Information and Documentation - Library Performance Indicators Draft ISO/FDIS 11620: 1997 (E). More details. Poll, Roswitha; Boekhorst, Peter te. Measuring Quality: International Guidelines for Performance Measurement in Academic Libraries . IFLA Publications 76, Munich, 1996.

72. Bienvenido A La Web De Metransa Utillajes para m¡quinas curvadoras y m¡quinas herramienta (carriles, carriles de altura, mandrinos, contracarriles y matrices de curvado). http://www.metransa.com/marcos.html

73. Chapter 10: Dictionaries right left . Click here for feedback 10.4 Sparse matrices. In Section 8.14, we used a list of lists to represent a matrix. That is http://www.ibiblio.org/obp/thinkCSpy/chap10.htm

Chapter 10 Click here for feedback Dictionaries The compound types you have learned about strings, lists, and tuples use integers as indices. If you try to use any other type as an index, you get an error. Dictionaries are similar to other compound types except that they can use any immutable type as an index. As an example, we will create a dictionary to translate English words into Spanish. For this dictionary, the indices are strings One way to create a dictionary is to start with the empty dictionary and add elements. The empty dictionary is denoted 'one' 'uno' 'two' 'dos' The first assignment creates a dictionary named ; the other assignments add new elements to the dictionary. We can print the current value of the dictionary in the usual way: print 'one' 'uno' 'two' 'dos' The elements of a dictionary appear in a comma-separated list. Each entry contains an index and a value separated by a colon. In a dictionary, the indices are called keys , so the elements are called key-value pairs Another way to create a dictionary is to provide a list of key-value pairs using the same syntax as the previous output: 'one' 'uno' 'two' 'dos' 'three' 'tres' If we print the value of again, we get a surprise:

74. 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 TimeSeries (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/

var thisName = "Home" General VisiCube Support Datamology Company General Home Site Map Survey VisiCube Why VisiCube? Advantages... Data Microscope Collaboration Graphing Hypercubes ... Demos Samples... Box Array Quantile/Box Plot Quantile Array 2D Scatter Plot ... Product Uses Support Download Trial Purchase Support Policy ... Knowledge Base Contact... Report Problem Request Feature Ask Question Datamology Definition Data Exploration Data Analysis EDA ... Scientist's Debate Company Mission Contact Careers Explore your data! DM_menuEntry("index.shtml" , "Home" ) DM_menuEntry("sitemap.shtml", "Site Map") DM_menuEntry("survey.shtml" , "Survey") The Datamology Home Page Welcome Welcome to The Datamology Company, the makers of VisiCube (the Data Microscope), where we are dedicated to providing you with software which truly facilitates the study of information. VisiCube is a graphical exploratory data analysis tool designed to aid you in research without depending on mathematical modeling. It is free, runs on Windows-based PCs, and can be downloaded directly from this website The Datamology Company is an employee-owned software company that was founded on January 1, 2003, by a team of veteran developers with an average of 30 years experience in the software industry. Our previous software projects span the entire world of computer-assisted datamology including data management, data reporting, and data warehousing.

75. Networks And Matrices Networks and matrices. Networks can be represented as graphs or matrices. For example, here is a graph Matrix Algebra. matrices are basically tables. http://www.analytictech.com/networks/matrices.htm

Networks and Matrices Networks can be represented as graphs or matrices. For example, here is a graph: We can also record who is connected to whom on a given social relation via what is called an adjacency matrix. The adjacency matrix is a square actor-by-actor matrix like this: And Bil Car Dan Ele Fra Gar Andy Bill Carol Dan Elena Frank Garth If the matrix as a whole is called X, then the contents of any given cell are denoted x ij . For example, in the matrix above, x ij = 1, because Andy likes Bill. Note that this matrix is not quite symmetric (x ij not always equal to x ji Anything we can represent as a graph, we can also represent as a matrix. For example, if it is a valued graph, then the matrix contains the values instead of 0s and 1s. By convention, we normally record the data so that the row person "does it to" the column person. For example, if the relation is "gives advice to", then xij = 1 means that person i gives advice to person j, rather than the other way around. However, if the data not entered that way and we wish it to be so, we can simply transpose the matrix. The transpose of a matrix X is denoted X'. The transpose simply interchanges the rows with the columns. Matrix Algebra Matrices are basically tables. They are ways of storing numbers and other things. Typical matrix has rows and columns. Actually called a 2-way matrix because it has two dimensions. For example, you might have respondents-by-attitudes. Of course, you might collect the same data on the same people at 5 points in time. In that case, you either have 5 different 2-way matrices, or you could think of it as a 3-way matrix, that is respondent-by-attitude-by-time.

76. Tim Davis: UF Sparse Matrix Collection : Sparse Matrices From A Wide Range Of Ap A collection of large sparse matrices from many scientific disciplines with links and software pieces to operate on matrix data structures. http://www.cise.ufl.edu/research/sparse/matrices/

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 University of Florida Sparse Matrix Collection: Note: the matrices are no longer available via ftp. UF sparse matrix collection in Harwell-Boeing format UF sparse matrix collection in MATLAB format list of matrix names, sizes, and basic attributes list of matrices and their type (Harwell-Boeing format) The UF Sparse Matrix Collection is a large set of sparse matrices from a wide range of problems. As of October 2003, it contains 1179 matrices. The smallest is 5-by-5 with 19 nonzero entries, and the largest is 5.1 million-by-5.1 million, with 99.2 million entries. To cite this collection, use the following: T. Davis, University of Florida Sparse Matrix Collection, http://www.cise.ufl.edu/research/sparse/matrices NA Digest , vol. 92, no. 42, October 16, 1994, NA Digest , vol. 96, no. 28, July 23, 1996, and NA Digest , vol. 97, no. 23, June 7, 1997.

77. Substitution Matrices Scoring Systems. Logodds Substitution matrices for Scoring Amino-Acid Alignments. The relationship between BLOSUM and PAM substitution matrices. 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.

78. GB XPOINT Video Audio Devices Manufacturers of matrices, switchers, distribution amplifiers, video and audio equipment. http://www.gbxpoint.it

***Aggiornate 34 nuove schede tecniche relative a 34 modelli su catalogo*** MS8B nuova matrice 8x8 Video Composito + Audio Stereo Bilanciato*** MS16B nuova matrice 16x16 Video Composito + Audio Stereo Bilanciato***...in arrivo Generatori di logos LG100 ed LG200 ! *** Schede Tecniche: SDP SKxx VDxSDI Video Composito e Audio stereo Bilanciato. Matrice di commutazione 16 ingressi su 16 uscite Video Composito e Audio Stereo Bilanciato. Matrice SDI (Serial Digital Interface) da 16 ingressi con LOOP "bufferato" su 16 uscite digitali 4:2:2, SMPTE259 . Commutazione sincrona al segnale presente sul canale dedicato SY-IN. Uscita Preview di controllo stato segnali d'ingresso. MS16 SDI: matrice Serial digital Interface SDP Convertitore da SDI a Video Composito, S-VHS, RGB, YUV (PAL), livello video regolabile. Apparecchiature dalle ridotte dimensione: SDP: Convertitore SDI to PAL Fast Entrambe le linee dispongono di un buffer profondo 4096 bytes.

79. Entrez Help Document: Summary Matrices Summary matrices. This document provides the following summary tables for the Entrez Nucleotide, Protein, Genome, Structure, and Popset data domains http://www.ncbi.nlm.nih.gov/entrez/query/static/help/Summary_Matrices.html

Entrez Help Document PubMed Entrez BLAST OMIM ... Structure Last modified : July 18, 2000 Summary Matrices This document provides the following summary tables for the Entrez Nucleotide, Protein, Genome, Structure, and Popset data domains: Limits Available by Database Search Fields Available by Database Search Field Desriptions and Qualifiers Display Formats The PubMed help document contains separate information about the Limits Search Fields , and Display Formats available for that database. Back to the Entrez Help Document Limits Available by Database Databases Limits Nucleotide Protein Genome Structure PopSet Search Fields Yes Yes Yes Yes Yes Exclude ESTs Yes No No No No Exclude STSs Yes No No No No Exclude GSSs Yes No No No No Exclude Working Draft Yes No No No No Exclude Patents Yes Yes No No No Molecule Type Yes No No No No Gene Location Yes Yes No No No Segmented Sequences Yes Yes No No No Database Source Yes Yes No No No Modification Date Yes Yes No No No Back to the Entrez Help Document Search Fields Available by Database Databases Search Field Descriptions and Qualifiers Nucleotide Protein Genome Structure PopSet Accession Yes Yes Yes Yes Yes All Fields Yes Yes Yes Yes Yes Author Name Yes Yes Yes Yes Yes EC/RN Number Yes Yes Yes Yes Yes Feature Key Yes No Yes No Yes Filter Yes Yes Yes Yes Yes Gene Name Yes Yes Yes No Yes Issue Yes Yes Yes Yes Yes Journal Name Yes Yes Yes Yes Yes Keyword Yes Yes Yes No Yes Modification Date Yes Yes Yes Yes Yes Molecular Weight No Yes No No No Organism Yes Yes Yes Yes Yes Page Number Yes Yes Yes Yes Yes Primary Accession Yes Yes Yes No Yes Properties Yes Yes Yes No Yes Protein Name Yes Yes Yes No Yes Publication Date Yes Yes Yes Yes Yes SeqID String

80. Welcome To Adobe GoLive 6 A relational database of phylogenetic trees and the data matrices used to generate them from published research papers. Includes animals, plants, and fungi. http://www.treebase.org/treebase/

Sorry! The TreeBASE server experienced a massive hard drive failure. New hardware has been ordered and will be running as soon as possible. Meanwhile, send me your data by email

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