121. Matrices In Chemistry Balancing Equations Using matrices. NOTE this application requires that you have a calculator capable of doing matrices. Most if http://www.shodor.org/unchem/math/matrix/

HOME Course Chapters Calculator Fundamentals Mathematics Review Numbers and their Properties Numbers in Science ... Advanced Concepts Section Tests Pre-test Post-test Useful Materials Glossary Online Calculators Redox Calculator Kinetics Arrhenius Calculator Thermodynamics Calculator Nuclear Decay Calculator ... Nomenclature Calculator Related Information Links Texas Instruments Calculators Casio Calculators Sharp Calculators Hewlett Packard Calculators ... Contact Webmaster Balancing Equations Using Matrices NOTE: this application requires that you have a calculator capable of doing MATRICES. Most if not all graphical calculators have this capability. This reading uses the Texas Instrument TI-82 Graphical Calculator as an example. Early on in your chemistry studies, you will have ample opportunity to balance equations! This is a fundamental skill in chemistry, as you might have noticed from the short reading in stoichiometry! Balancing equations means writing chemical equations such that the amount of stuff you start with in the reaction equals the amount of stuff you end up with as a product. In other words, if I start baking bread with 10 pounds of flour, I should end up with 10 pounds of bread, unless some is lost onto the floor or if some of it goes up in smoke! A simple example goes a long way. We can form water by combing hydrogen gas (H

122. Osni Marques' Home Page BLZPACK uses the block Lanczos algorithm to solve (generalized) eigenvalue problems, HLZPACK uses the Lanczos algorithm to solve Hermitian eigenvalue problems, and SKYPACK implements algorithms for matrices having a skyline structure. By Osni Marques. http://crd.lbl.gov/~osni/#Software

Osni Marques Address: Lawrence Berkeley National Laboratory 1 Cyclotron Road, MS 50F-1650 Berkeley, CA 94720-8139, USA E-mail: oamarques@lbl.gov Phone: Fax: Interests Papers Applications Software ... Other Research and Interests Numerical methods for the LAPACK and ScaLAPACK libraries. The DOE ACTS Collection and the NSF NPACI Project. Algorithms for the solution of large, sparse, eigenvalue problems. High-end scientific computing. Selected Papers A Computational Strategy for the Solution of Large Linear Inverse Problems in Geophysics , with T. Drummond and D. W. Vasco. International Parallel and Distributed Processing Symposium (IPDPS), Nice, France, 2003. Resolution, Uncertainty and Whole Earth Tomography , with D. W. Vasco and L. R. Johnson. Journal of Geophysical Research, Solid Earth, 108, Jan 10, 2003. The Advanced Computational Testing and Simulation (ACTS) Toolkit: What can ACTS do for you? , with T. Drummond. Technical Report LBNL-50414, 2002. On Computing Givens Rotations Reliably and Efficiently , with D. Bindel, J. Demmel and W. Kahan. ACM TOMS, 28:206-238, 2002. Geodetic Imaging: High Resolution Reservoir Monitoring using Satellite Interferometry , with D. W. Vasco, C. Wicks Jr. and K. Karasaki. Geophysical Journal International, 200:1-12, 2001.

123. Z-Matrices Lab Activity ChemViz. Lab Activities. Welcome to the Zmatrices Lab Activity. Lab Activities. Z-matrices; Basis Sets; Geometry Optimizations; Ionization Energies Support Materials. http://www.shodor.org/chemviz/zmatrices/

ChemViz Lab Activities Welcome to the Z-Matrices Lab Activity Home Readings Overview Atomic Orbitals Lab Activities Z-matrices Basis Sets Geometry Optimizations Ionization Energies Support Materials Interactive Tools Glossary of Terms Quick Guide to DISCO Output File Related Links ChemViz Computational Chemistry SUCCEED's Computational Chemistry Developers' Tools What's New? Discussion Board Team Members Email the Group ... Contact Webmaster Table of Contents Student Materials Introduction Objectives Background Reading Procedure ... References/Support Materials Teacher Materials Additional Background Materials Standards First year chemistry curriculum concepts ... Second year chemistry curriculum concepts Developed by The Shodor Education Foundation, Inc. in cooperation with the National Center for Supercomputing Applications

124. Stiffi Carbon Fiber Paintball Barrels By Site Manufacturing CA, USA. Compression molding, hand layup and Autoclave. (Fibers Carbon Graphite, E S-2 Glass, Aramid Kevlar®, along with a variety of matrices). R D, Engineer and Manufacture composite products. http://www.sitemfg.com

STIFFI CARBON FIBER PAINTBALL BARRELS BY SITE MANUFACTURING SITE MANUFACTURING PRODUCES PROFESSIONAL QUALITY CARBON FIBER PAINTBALL PRODUCTS. ENTER HOME OF THE STIFFI BARREL

125. Not Positive Definite Matrices--Causes And Cures Not Positive Definite matricesCauses and Cures. The seminal work on dealing with not positive definite matrices is Wothke (1993). http://www.gsu.edu/~mkteer/npdmatri.html

Not Positive Definite MatricesCauses and Cures The seminal work on dealing with not positive definite matrices is Wothke (1993) . The chapter is both reabable and comprehensive. This page uses ideas from Wothke, from SEMNET messages, and from my own experience. The Problem There are four situations in which a researcher may get a message about a matrix being "not positive definite." The four situations can be very different in terms of their causes and cures. First, the researcher may get a message saying that the input covariance or correlation matrix being analyzed is "not positive definite." Generalized least squares (GLS) estimation requires that the covariance or correlation matrix analyzed must be positive definite, and maximum likelihood (ML) estimation will also perform poorly in such situations. If the matrix to be analyzed is found to be not positive definite, many programs will simply issue an error message and quit. Second, the message may refer to the asymptotic covariance matrix. This is not the covariance matrix being analyzed, but rather a weight matrix to be used with asymptotically distribution-free / weighted least squares (ADF/WLS) estimation.

126. Analysis Of Incomplete Datasets: Estimation Of Mean Values And Covariance Matric A regularized expectationmaximization (EM) algorithm for the estimation of mean values and covariance matrices and for the imputation of missing values in large, incomplete datasets. http://www.gps.caltech.edu/~tapio/imputation/

Analysis of incomplete datasets: Estimation of mean values and covariance matrices and imputation of missing values Purpose Installation Module descriptions Possible modifications Purpose What follows is a collection of Matlab modules for the estimation of mean values and covariance matrices from incomplete datasets, and the imputation of missing values in incomplete datasets. The modules implement the regularized EM algorithm described in T. Schneider, 2001: Analysis of incomplete climate data: Estimation of mean values and covariance matrices and imputation of missing values Journal of Climate The EM algorithm for Gaussian data is based on iterated linear regression analyses. In the regularized EM algorithm, ridge regression with generalized cross-validation replaces the conditional maximum likelihood estimation of regression parameters in the conventional EM algorithm. The implementation of the regularized EM algorithm is modular, so that the modules that perform the ridge regression and the generalized cross-validation can be exchanged for other regularization methods and other methods of determining a regularization parameter. Per-Christian Hansen's Regularization Tools contain Matlab modules implementing a collection of regularization methods that can be adapted to fit into the framework of the EM algorithm. The generalized cross-validation modules of the regularized EM algorithm are adapted from Hansen's generalized cross-validation modules.

127. Matrices matrices. We are often interested in data that is most naturally written as a matrix or array. For example, in chapter 1 we used matrices to represent images. http://www.math.montana.edu/frankw/ccp/multiworld/matrices/matrices/body.htm

Matrices We begin by reviewing matrix operations and the way that they are expressed using your computer algebra system. Open your computer algbera system now by clicking its icon in the navigation frame. We are often interested in data that is most naturally written as a matrix or array For example, in chapter 1 we used matrices to represent images. Matrices are also discussed in the section on matrices in the mathematical infrastructure. In that section we discuss adding two matrices and multiplying a matrix by a real number. Vectors can be thought of as matrices Vectors are often thought of as either a matrix with one row or as a matrix with one column. We call a vector a row vector when we think of it as a matrix with one row and a column vector when we think of it as a matrix with one column. The transpose of a matrix It is sometimes useful to exchange the roles of the rows and columns. For example, consider the two matrices written below. The lefthand matrix describes the traffic flow each morning as commuters drive from their homes in three towns Oak, Elm, and Maple to their jobs at three companies ABC Co., DEF Co., and GHI Co. The table on the right shows the traffic each afternoon as commuters return home. Notice that the rows of the first matrix become the columns of the second matrix. This matrix is called the transpose of the first matrix.

128. Welcome To Ming Gu's Homepage Codes available from author to quickly update singular value decompositions, solve banded plus semiseparable systems of linear equations, and compute eigenvalues symmetric blockdiagonal plus semiseparable matrices. http://math.berkeley.edu/~mgu/

Ming Gu Associate Professor. Office: 861 Evans Department of Mathematics University of California Berkeley, CA 95472 Phone: (510) 642-3145 Email: mgu@math.berkeley.edu Biographical Sketch: Ming Gu received his PhD (1993) degree in Computer Science from Yale University. He was a Morrey Assistant Professor at UC Berkeley from 1993 to 1996 and a professor at UCLA since 1996. He joined the Berkeley faculty in July 2000. His research interests include fast algorithms in numerical linear algebra, adaptive filtering, system and control theory, and differential and integral equations. Awards: Alfred P. Sloan Research Fellow, 1998. The SIAM Activity Group on Linear Algebra Prize 1997 (with S. Eisenstat), awarded for the best paper in applied linear algebra worldwide written in the last three years. The NSF CAREER Award, 1997. The Faculty Early Career Development (CAREER) program ``combines in a single program the support of research and education of the highest quality and in the broadest sense.'' The Householder Award 1996, awarded for the best Ph.D. thesis in numerical algebra written since January 1, 1993. Topics in the thesis included efficient algorithms for eigenvalue problems and rank-revealing QR factorizations.

129. Mathematics And Statistics - Operator Algebras And Random Matrices Operator Algebras and Random matrices Conference, 2330 July 2004, Ambleside. Print this page. LMS workshop on free semigroup algebras http://www.maths.lancs.ac.uk/department/info/news/opAlgebra

130. Supported Clusters Research on clusters and nanosystems has the general aim of understanding the properties of matter at small sizes (typically less than 1000 atoms) and its interaction with surfaces. Novel methods are developed to produce and characterize clusters and nanosystems free or deposited on surfaces and in matrices. http://ipn2.epfl.ch/GPAS/

Welcome to the web site of the Cluster and Nanosystems Group at the Institute of Physics of Nanostructures at EPFL Research on clusters and nanosystems has the general aim of understanding the properties of matter at small sizes (typically less than 1000 atoms) and its interaction with surfaces. Novel methods are developed to produce and characterize clusters and nanosystems free or deposited on surfaces and in matrices. Postal address: Institut de Physique des Nanostructures FSB EPFL (École Polytechnique Fédérale de Lausanne) CH-1015 Lausanne Switzerland Phone: +41 21 693 3320, Fax: +41 21 693 3604

131. REDIRECTION... Steve Baker s web site has moved Please update your links and bookmarks. In just a few seconds, I ll redirect you to it s new home at http//sjbaker.org/steve. http://web2.iadfw.net/sjbaker1/matrices_can_be_your_friends.html

Steve Baker's web site has moved Please update your links and bookmarks. In just a few seconds, I'll redirect you to it's new home at http://sjbaker.org/steve

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

The Matrix Computation Toolbox by Nicholas J. Higham The Matrix Computation Toolbox is a collection of MATLAB M-files containing functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search optimization. Various other miscellaneous functions are also included. This toolbox supersedes the author's earlier Test Matrix Toolbox (final release 1995). The toolbox was developed in conjunction with the book Accuracy and Stability of Numerical Algorithms SIAM Second edition , August 2002, xxx+680 pp.). That book is the primary documentation for the toolbox: it describes much of the underlying mathematics and many of the algorithms and matrices (it also describes many of the matrices provided by MATLAB's gallery function). The picture on the left, produced by toolbox function pscont , shows a view of pseudospectra of the matrix gallery('triw',11) The toolbox is distributed under the terms of the GNU General Public License (version 2 of the License, or any later version) as published by the Free Software Foundation. The toolbox has been tested under MATLAB 6.1 (R12.1) and MATLAB 6.5 (R13). For how to overcome a minor incompatibility with MATLAB 6.1 and earlier see the updates link below.

133. Matrix Reference Manual Matrix Reference Manual. Introduction. This manual contains reference information about linear algebra and the properties of matrices. Special matrices. http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/intro.html

Matrix Reference Manual Introduction This manual contains reference information about linear algebra and the properties of matrices. The manual is divided into the following sections: Properties Eigenvalues : Theorems and matrix properties relating to eigenvalues and eigenvectors. Special Relations Decompositions : Decomposing matrices as sums or products of simpler forms. Identities : Useful equations relating matrices. Equations : Solutions of matrix equations Differentiation : Differentiating expressions involving matrices whose elements are functions of an independent variable. Stochastic : Statistical properties of vectors and matrices whose elements are random numbers. Signals : Properties of observation vectors and covariance matrices from stochastic and deterministic signals. Examples: 2#2 : Examples of 2#2 matrixes with graphical illustration of their properties. Formal Algebra Main Index The Matrix Reference Manual is written by Mike Brookes , Imperial College, London, UK. Please send any comments or suggestions to mike.brookes@ic.ac.uk

134. Multivariate Analyses Fortran 90 codes for univariate and multivariate random number generation, computation of simple statistics, covariance matrices, principal components analysis, multiple regression, and jacknife crossvalidation, by Dan Hennen. http://www.esg.montana.edu/eguchi/multivariate/#Fortran

Environmental Analyses (BIOL 505, Spring 2002) Montana State University, Bozeman Class hours: Monday/Wednesday/Friday 14:10 - 15:00 Last modified: Fri Mar 15 11:46:16 MST 2002 This is the homepage for Biology 505, Spring 2002 (D. Goodman). This page will contain lecture notes, examples of programs (FORTRAN, Matlab, Java, and C), and any other relevant information to Dr. Goodman's lecture. For any suggestions and questions regarding this homepage, please email Tomo Eguchi Index: Contact Information Additional Information Lecture Notes Programming ... Data Contact Information: Dan Goodman: goodman@rivers.oscs.montana.edu Tomo Eguchi: eguchi@montana.edu Dan Hennen: hennen@torrent.msu.montana.edu Nicole Wagner: nwagner@montana.edu Eric Ward: eward@montana.edu Matt Rinella: mrinella@montana.edu Additional information: Here are some books and other additional papers/summary that are relevant to the class (in a random order): Multivariate Analysis , K. V. V. Mardia, J. T. Kent, and J. M. Bibby. Academic Press, 1980. (Recommended by Dr. Goodman) Applied Linear Statistical Models , J. Neter, M. H. Kutner, C. J. Nachtsheim, and W. Wasserman. IRWIN, 1996.

135. Practical Transformation Matrices In Crystallography Practical transformation matrices in crystallography. by F. Otálora JD. MartínRamos. When the reference system for a crystal http://lec.ugr.es/trans/

Practical transformation matrices in crystallography by When the reference system for a crystal (a,b,c) is changed to a new one ( a b c ) keeping the same origin, the values of the spatial coordinates within the lattice, the Miller indices of crystal faces, the indices of diffraction spots, etc. must be recomputed. The use of transformation matrices is very useful for this computing work, but much care must be taken in using the right transformation rules. This page is designed to provide a practical set of such rules for reference as well as helping you in the computation of transforms through an on-line Transformations Calculator Let A be the matrix containing the old reference system and B the matrix containing the new reference system. Then M is the matrix converting A into B B MA that is, a 3x3 matrix containing the scalar product of the vectors making up the old and new reference systems. M a a a b a c b a b b b c c a c b c c Fig 1. Example of transforming a general triclinic reference system into an orthonormal one. By multiplying both terms of the equation by the inverse matrix M M B MM A A so the transformation from the new reference system to the old one is A M B The practical uses of these transformations are summarizaed below (superindex t indicating the transpose matrix): Transformation of Miller indices or reflexions ( H t (h,k,l)

136. Discrete Tomography Theory behind combinatorial reconstruction of matrices from horizontal and vertical projections for interpretion of Xray crystallography coordinates, from Laboratoire de Recherche en Informatique, Paris University, France. http://www.lri.fr/~durr/Xray/

Discrete Tomography This page addresses the problem of reconstructing polyatomic or monoatomic structures from discrete X-Rays. Tomography is the area of reconstructing objects from projections. In discrete tomography , an object T we wish to reconstruct is a set of cells of a multidimensional grid. We perform measurements of T , each one involving a projection that determines the number of cells in T on all lines parallel to the projection's direction. Given a finite number of such measurements, we wish to reconstruct T or, if unique reconstruction is not possible, to compute any object consistent with these projections. Open problems Programs Reconstruct hv-convex polyominoes Reconstruct tilings of vertical dominoes and cells

137. Available Matrices For Bioccelerator Searches Available matrices For Bioccelerator Searches. Gonnet Series. gon30, gon60, gon90, gon160, gon120, gon250, gon200, gon350. gon500, gon750, gon1000, gonnet. Blossum Series. http://eta.embl-heidelberg.de:8000/misc/mat/

Available Matrices For Bioccelerator Searches Gonnet Series gonnet Blossum Series blosumn Pam Series Identity Series identity Bin Series Home Last Updated: Fri Jan 8 13:55:49 1999

138. Research Computes a few (algebraiclly) smallest or largest eigenvalues of large symmetric matrices. http://www.ms.uky.edu/~qye/software.html

S OFTWARE P AGE of Q IANG Y E EIGIFP.m A matlab program that computes a few ( algebraiclly ) smallest or largest eigenvalues of a large symmetric matrix A or a symmetric matrix pencil (A, B): A x = lambda x or A x = lambda B x where It is a black-box implementation of the inverse free preconditioned Krylov subspace method of G. Golub and Q. Ye An Inverse Free Preconditioned Krylov Subspace Method for ... Problems SIAM Journal on Scientific Computing, 24:312-334. Features A two level iteration with a projection on Krylov subspaces generated by a shifted matrix A- B in the inner iteration; Adaptive choice of inner iterations; A preconditioning technique based on a congruence transformation to accelerate convergence; A built-in preconditioner using threshold ILU factorization Particularly suitable for problems where any of the following applies: a) factorization of B (i.e. inverting B) is difficult; b) factorization of a shifted matrix A- B (i.e. inverting it) is difficult; c) no a priori information is available on the location of the spectrum sought. Usage lambda , x] = eigifp A): computes the ( algebraiclly ) smallest eigenvalue /eigenvector of A;

139. PlanetMath: Hadamard Matrix A few examples of Hadamard matrices are. Hadamard matrices are common in signal processing and coding applications. Hadamard matrix is owned by Koro. http://planetmath.org/encyclopedia/HadamardMatrix.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List Hadamard matrix (Definition) An matrix is a Hadamard matrix of order if the entries of are either or and such that where is the transpose of and is the order identity matrix In other words, an matrix with only and as its elements is Hadamard if the inner product of two distinct rows is and the inner product of a row with itself is A few examples of Hadamard matrices are These matrices were first considered as Hadamard determinants , because the determinant of a Hadamard matrix satisfies equality in Hadamard's determinant theorem, which states that if is a matrix of order where for all and then Property 1: The order of a Hadamard matrix is or where is an integer.

140. The RRGIBBS Home Page Fortran 95 codes by Karin Meyer RRGIBBS does simple random regression analyses via Gibbs sampling, and PDMATRIX makes matrices positive definite. http://agbu.une.edu.au/~kmeyer/rrg_main.html

Introduction Random regression (RR) models have become a popular choice for the analysis of longitudinal data or 'repeated' records. Typically, analyses require numerous parameters, i.e. (co)variances between RR coefficients and measurement error variances, to be estimated, especially if the model of analysis includes additional random effects such as maternal effects. Programs for RR model analysis using restricted maximum likelihood (REML) are available. However, the high computational demands of REML analyses for RR models severely limit the feasibility of RR analyses for data sets sufficiently large to support estimation of the pertaining (co)variance components, in particular for models fitting many RR coefficients. Bayesian analyses using Gibbs sampling provide an alternative which is markedly simpler to implement than REML. Whilst the range of models which can be accommodated via Gibbs sampling may be more restrictive and the total computing time required may be longer than for corresponding REML analyses, memory requirements are substantially less. Hence Bayesian methodology readily facilitates large scale analyses. Apart from these practical advantages, of course, it provides estimates of complete sampling distributions rather than just simple point estimates. Purpose RRGIBBS performs a single task : the analysis of a simple class of RR models using Bayesian methodology. Models may involve

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