41. Linear Algebra: Table Of Contents Dr. Min Yan is a Mathematician in Hong Kong University of Science and Technology. He teaches linear algebra in this semester http://algebra.math.ust.hk/course/content.shtml

Linear Algebra Table of Contents System of Linear Equations System of Linear Equations Augmented Matrix Row Operation Gaussian elimination and back substitution Extra: The three operations do not change solutions Row operation Row Echelon Form Row echelon form Shape of row echelon form Computing row echelon form Reduced row echelon form Extra: Reduced row echelon form vs. General solution Existence Existence of solutions for fixed right side Existence of solutions for any right side Uniqueness Structure of solutions Uniqueness of solutions A Basic Linear Algebra Principle Implication of existence/uniqueness on size Implication of size on existence/uniqueness Linear Transformation and Matrix Vector and Matrix Euclidean vector and euclidean space Extra: Vector addition is given by parallelogram Matrix Some matrix notations and terminologies Linear Transformation Transformation Extra: Root-Polynomial transformation Matrix transformation Linear transformation Extra: Matrix transformations are linear Linearity in picture Linear transformation = matrix transformation Extra: Matrix of a linear transformation Onto Range and existence Onto and always existence One-to-one One-to-one and uniqueness Kernel and uniquess Composition and Matrix Multiplication Composition of transformations Multiplication of matrices Extra: Composition of linear transformations is linear Properties of matrix multiplication Composition/multiplication mixed with addition and scalar multiplication Inverse Inverse transformation Extra: Criterion for invertibility of a transformation Inverse matrix Inverse of 2 by 2 matrix Computation of inverse matrix ... Properties of inverse Extra:

42. Lyryx Learning Inc. Contains narrated and animated lessons, interactive exploration and computational tools, and an assessment system providing feedback to guide student learning. http://lila.lyryx.com/

43. Math Forum: Linear Algebra The best Internet resources for linear algebra classroom materials, software, Internet projects, and public forums for discussion. http://mathforum.org/linear/linear.html

Linear Algebra Back to Math by Subject Math by Subject K12 Topics algebra arithmetic calculus discrete math geometry pre-calculus prob/stat Advanced Topics analysis calculus diff. equations game theory discrete math geometry (coll.) geometry (adv.) linear algebra modern algebra num. analysis Linear Algebra - Internet Resources See also the Math Forum's Internet Mathematics Library: Linear Algebra Classroom materials for teachers and students Selected linear algebra Internet resources for the classroom including activities and interactive resources. Software for linear algebra Publicly available software and publishers online. Internet projects Activities for students and lovers of linear algebra. Public forums Mailing lists and newsgroups sponsored by the Forum and others where mathematicians,teachers, and students trade ideas about linear algebra. Home The Math Library Quick Reference Search ... Help http://mathforum.org/ The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies

44. Topics In Linear Algebra An approach unifying the notions of system of equations, matrix inversion, and linear programming. http://home.ubalt.edu/ntsbarsh/opre640a/partXII.htm

Unification of System of Linear Equations, Matrix Inversion, and Linear Programming Europe Site Site for Asia Site for Middle East UK Site ... USA Site This site extends the existing one-way connections among the solving linear systems of equations, matrix inversion, and linear programming. The additional linkages empower the user to understand the wholeness and manifoldness of these topics. They also assist the user to model and solve a problem modeled as any one of the above topics by having access to a computer package solver. The goals are theoretical unification as well as advancements in applications. Illustrative numerical examples are presented. Professor Hossein Arsham To search the site , try E F ind in page [Ctrl + f]. Enter a word or phrase in the dialogue box, e.g. " inverse" or " equations" If the first appearance of the word/phrase is not what you are looking for, try F ind Next MENU Introduction LP Problem Solved by System of Equation Solver System of Equations Solution by LP Solver Solving for the Inverse of a Matrix Using LP Solver ... References and Further Readings Companion Sites: Linear Optimization Solvers to Download Success Science Leadership Decision Making Linear Programming (LP) and Goal-Seeking Strategy ... Decision Science Resources Introduction Linear programming (LP), Linear systems of equations, and Matrix inversion are often favorite topics for both instructors and students. The ability to solve these problems by Gauss-Jordan pivoting (GJP), the widespread availability of software packages, and their wide range of applications make these topics accessible even for students with relatively weak mathematical backgrounds. The typical textbooks on LP usually devote separate sections for each topic. However, the relationships among these closely related topics are often not presented or thoroughly discussed. This article extends the existing one-way connections among these topics to construct a comprehensive two-way relationship as in the following figure. For each topic, it is shown how the problem may be modeled and solved by either of the associated methodologies.

45. Linear Algebra Toolkit This Linear Algebra Toolkit is comprised of the modules listed below. Each module is designed to help a linear algebra student learn and practice a basic linear algebra http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi

Linear Algebra Toolkit - Main Page v. 1.23b This Linear Algebra Toolkit is comprised of the modules listed below . Each module is designed to help a linear algebra student learn and practice a basic linear algebra procedure, such as Gauss-Jordan reduction, calculating the determinant, or checking for linear independence. Click here for additional information on the toolkit. MODULES Systems of linear equations and matrices Row operation calculator Interactively perform a sequence of elementary row operations on the given m x n matrix A. Transforming a matrix to row echelon form Find a matrix in row echelon form that is row equivalent to the given m x n matrix A. Transforming a matrix to reduced row echelon form Find the matrix in reduced row echelon form that is row equivalent to the given m x n matrix A. Solving a linear system of equations Solve the given linear system of m equations in n unknowns. Calculating the inverse using row operations Find (if possible) the inverse of the given n x n matrix A. Determinants Calculating the determinant using row operations Calculate the determinant of the given n x n matrix A.

46. Linear Algebra, Infinite Dimensions, And Maple A textbook by James Herod. http://www.math.gatech.edu/~herod/Hspace/Hspace.html

Linear Algebra, Infinite Dimensions, and Maple Preface for these notes. Chapters 1 and 2 A Decomposition for Matrices Exp(tA) Chapters 3 and 4 Self Adjoint Transformations in Inner-Product Spaces The Gerschgorin Circle Theorem Chapters 5 and 6 Convergence Orthogonality and Closest Point Projection Chapters 7 and 8 Orthonormal Vectors Chapters 9 and 10 The Finite Dimensional Paradigm Bounded Linear Maps from E to C Chapters 11 and 12 Applications to Differential Equations The Simple Paradigm from E to E Chapters 13 and 14 Adjoint Operators Compact Sets Chapters 15 and 16 Compact Operators The Space of Bounded Linear Operators Chapters 17 and 18 The Eigenvalue Problem Normal Operators and The More General Paradigm Chapters 19 and 20 Compact Operators and Orthonormal Families A Characterization of Compact Operators Chapters 21 and 22 The Fredholm Alternative Theorems Closed Operators Chapter 23 The Deficiency of A Chapter 24 A Problem in Control Chapter 25 Approximation in a Hilbert Space with a reproducing kernel Index for these notes. Maple Constructions for the Text Constructions in Chapters 1 and 2 Constructions in Chapters 3 and 4 Constructions in Chapters 5 and 6 Constructions in Chapters 7 and 8 ... Construction in Chapter 24

47. The Math Forum - Math Library - Linear Algebra The Math Forum's Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites relating to Linear http://mathforum.org/library/topics/linear/

Browse and Search the Library Home Math Topics Algebra : Linear Algebra Library Home Search Full Table of Contents Suggest a Link ... Library Help Subcategories (see also All Sites in this category Eigenvectors/Eigenvalues Matrices Systems of Linear Equations ... Vectors Selected Sites (see also All Sites in this category Linear Algebra - Math Forum Links to some of the best Internet resources for linear algebra: classroom materials, software, Internet projects, and public forums for discussion. more>> Linear and Matrix Algebra (Mathematics Archives) - University of Tennessee, Knoxville (UTK) An extensive list of links to sites with information about linear algebra, classified by level and type of resource. more>> Linear and Multilinear Algebra; Matrix Theory (Finite and Infinite) - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to linear and multilinear algebra and matrix theory. As presented to engineers and as the subject of much numerical analysis, this subject is Matrix Theory. To an algebraist or geometer, it is the theory of Vector Spaces. Linear algebra, sometimes disguised as matrix theory, considers sets and functions which preserve linear structure. In practice this includes a very wide portion of mathematics; thus linear algebra includes axiomatic treatments, computational matters, algebraic structures, and even parts of geometry; moreover, it provides tools used for analyzing differential equations, statistical processes, and even physical phenomena. History, applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.

48. Linear Algebra Glossary Includes definitions and examples of all basic concepts. http://people.scs.fsu.edu/~burkardt/html/linear_glossary.html

Linear Algebra Glossary This file defines common terms from linear algebra. TABLE OF CONTENTS A-Orthogonal Vectors Adjacency Matrix Adjoint Matrix Alternating Sign Matrix ... Zero One Matrix A-Orthogonal Vectors Two vectors u and v are said to be A-orthogonal if ( u, A * v ) = 0. Here A should be a positive definite symmetric matrix , which in turn guarantees that the expression ( u, A * v ) may be regarded as an inner product of the vectors u and v , with the usual properties. This concept is useful in the analysis of the conjugate gradient method Back to TABLE OF CONTENTS. Adjacency Matrix An adjacency matrix of an (undirected) graph is a matrix whose order is the number of nodes, and whose entries record which nodes are connected to each other by a link or edge of the graph. If two nodes I and J are connected by an edge, then A i,j =A j,i . All other entries of the matrix are 0. Thus, an adjacency matrix is a zero-one matrix . The usual convention is that a node is not connected to itself, and hence the diagonal of the matrix is zero. The product A =A*A is a matrix which records the number of paths between nodes I and J . If it is possible to reach one node from another, it must be possible in a path of no more than

49. Linear Algebra File Format PDF/Adobe Acrobat Quick View http://www.openmathtext.org/lecture_notes/new_linearalgebra.pdf

50. Abstract And Linear Algebra • Index Page A forum for students on abstract algebra and linear algebra. http://www.math.miami.edu/forum/algebra/

51. 18.06 Linear Algebra Videos Fall 1999 Offers online video lectures for MIT s Linear Algebra course. Topics include geometric properties, using matrices, permutations, pivot variables, subspaces, Cramer s Rule, and Eigenvalues. http://web.mit.edu/18.06/www/Video/video-fall-99.html

Professor Strang's Linear Algebra Class Lecture Videos Welcome to the Videotaped Lectures webpage for MIT's Course 18.06: Linear Algebra . Standard Athena workstation configurations will allow you to view the 18.06 lecture videos. If you wish to access the videos from a Mac or PC, you should download the RealPlayer. You do not need the Plus Version of the RealPlayer - the free RealPlayer will work fine. NOTE: We are aware that some users are unable to access these lectures even if they were able to in the recent past. We are working at resolving this problem. In the meantime, please try viewing the same lectures at OCW . We apologize for any inconvinience. Lecture #1: The Geometry of Linear Equations ( Lecture #19: Determinant Formulas and Cofactors ( Lecture #2: Elimination with Matrices ( Lecture #20: Cramer's Rule, Inverse Matrix, and Volume ( Lecture #3: Multiplication and Inverse Matrices ( Lecture #21: Eigenvalues and Eigenvectors ( Lecture #4: Factorization into A = LU ( Lecture #22: Diagonalization and Powers of A ( Lecture #5: Transposes, Permutations, Spaces R^n (

52. » Download Linear Algebra Download the latest version of Linear Algebra free. Performs computations associated with matrices. http://linear-algebra.findmysoft.com/

53. LAPACK Alternative source of LAPACK. http://www.cs.colorado.edu/~jessup/lapack/

Home Help Netlib Search ... Documentation Quick Links Linear Equation Computational Routines Linear Equation Driver Routines Symmetric Eigenproblem Driver Routines LAPACK Internet Interface and Search Engine LAPACK provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision. Release 3.0 of LAPACK introduces new routines, as well as extending the functionality of existing routines. For detailed information on the revisions, please refer to the LAPACK revisions info Contact Us LAPACK FAQ About the BLAS ... About this Site

54. Math Forum - Ask Dr. Math Archives: College Linear Algebra Equivalent Matrices 7/12/1996 What are equivalent matrices? How do I use them? Solving Problems Using Matrices 9/31/1995 Given a current x,y,z coordinate (i.e. 60,-60,-60) and http://mathforum.org/library/drmath/sets/college_linearalg.html

Ask Dr. Math College Archive Dr. Math Home Elementary Middle School High School ... Dr. Math FAQ TOPICS This page: linear algebra Search Dr. Math See also the Internet Library linear algebra COLLEGE Algorithms Analysis Algebra linear algebra ... Trigonometry Browse College Linear Algebra Stars indicate particularly interesting answers or good places to begin browsing. Equivalent Matrices What are equivalent matrices? How do I use them? Solving Problems Using Matrices Given a current x,y,z coordinate (i.e. -60,-60,-60) and an angle (i.e. 90 degrees) and a plane to rotate about (i.e. z), what's the formula to solve for x,y,z? Use of Tensors What are the uses and properties of tensors? 3-D Coordinate Vector Transformation What is the approach to take for transforming one coordinate system to another? 3D Geometry You can draw a line of minimum distance between and perpendicular to two lines in 3space. I know how to get the distance and direction of this line, but I want to locate the line in 3space so that I can find its midpoint. An Absorbing States Problem A mouse is in one of 4 rooms. If it finds cheese in the current room, it stays there; if not, it exits to another room at random. What is the probability it will get trapped? Are there any absorbing states?

55. Lanczos Codes to compute eigenvalues and eigenvectors using the Lanczos algorithm. http://www.netlib.org/lanczos/index.html

lanczos Click here to see the number of accesses to this library. lib for chapters of "Lanczos Algorithms" book volume 2 by Jane Cullum cullumj@lanl.gov and Ralph Willoughby file vol2.pdf.gz for same as lanczos/vol2, but as a single large PDF file size 1.6MB file vol2.ps.gz for same as vol2.pdf.gz, but PostScript instead of PDF size 800kB file hleval for distinct eigenvalue of a Hermitian matrix using Lanczos tridiagonalization without reorthogonalization file leval for distinct eigenvalues of a real symmetric matrix using Lanczos tridiagonalization file lsval for distinct singular values of a real, rectangular matrix using Lanczos tridiagonalization file hlemult for internal routines to generate real symmetric tridiagonal matrices for (lanczos/hleval) and (lanczos/hlevec) file hlevec for eigenvectors of a Hermitian matrix, called with the eigenvalues from (lanczos/hleval) file levec for eigenvectors of a real symmetric matrix, called with the eigenvalues from (lanczos/leval) file lemult for internal routines to generate real symmetric tridiagonal matrices for (lanczos/leval) and (lanczos/levec) file lesub for internal routines for (lanczos/leval) and (lanczos/levec) file lsvec for singular vectors of a real, rectangular matrix using singular values from (lanczos/lsval) file

56. Linear Algebra And Its Applications - Elsevier (Elsevier) Abstracts from vol.214 (1995), full text to subscribers. http://www.elsevier.com/locate/laa

57. Lanz Solves the large, sparse, symmetric generalized eigenproblem. http://www.netlib.org/lanz/index.html

lanz Click here to see the number of accesses to this library. lanz_file1.tgz for code, documentation, makefiles, etc. size 51 kilobytes file lanz_file2.tgz for code, documentation, makefiles, etc. size 169 kilobytes file for just code, no documentation size 464 kilobytes lang Fortran file size 4 kilobytes lang C # Installation of LANZ, depending on your architecture, may take up # to 3.5mb of disk space. After installing LANZ, if you desire, you # can delete all but one or two files created by the installation # process.

58. Osni Marques' Home Page Numerical Linear Algebra with Applications, 13643653, 2006. The Advanced CompuTational Software (ACTS) Collection, with T. Drummond. ACM TOMS, 31282-301 , http://crd.lbl.gov/~osni/

Osni Marques Address: Lawrence Berkeley National Laboratory 1 Cyclotron Road, MS 50F-1650 Berkeley, CA 94720-8139, USA E-mail: Phone: Fax: Interests Publications Applications Software ... Other Interests The DOE ACTS Collection and the DOE SciDAC Program Numerical methods for the LAPACK and ScaLAPACK libraries. Algorithms for the solution of large, sparse, eigenvalue problems. High-end scientific computing. Selected Publications Performance and Accuracy of LAPACK's Symmetric Tridiagonal Eigensolvers , jointly with J. Demmel, C. Voemel and B. Parlett. Submitted to SIAM J. Sci. Comput. State-of-the-art Eigensolvers for Electronic Structure Calculations of Large Scale Nano-systems , jointly with C. Voemel, S. Tomov, A. Canning, L.-W. Wang and J. Dongarra. To appear in Journal of Computational Physics. A Testing Infrastructure for Symmetric Tridiagonal Eigensolvers , jointly with J. Demmel, C. Voemel and B. Parlett. To appear in ACM TOMS. The Use of Bulk States to Accelerate the Band Edge State Calculation of a Semiconductor Quantum Dot , with C. Voemel, S. Tomov, L.-W.-Wang and J. Dongarra. Journal of Computational Physics, 223:774-782, 2007.

59. PlanetMath: Linear Algebra Linear algebra is the branch of mathematics devoted to the theory of linear structure. The axiomatic treatment of linear structure is based on the notions http://planetmath.org/encyclopedia/LinearAlgebra.html

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclopædia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About linear algebra (Topic) Linear algebra is the branch of mathematics devoted to the theory of linear structure . The axiomatic treatment of linear structure is based on the notions of a linear space (more commonly known as a vector space ), and a linear mapping . Broadly speaking, there are two fundamental questions considered by linear algebra: the solution of a linear equation , and diagonalization , a.k.a. the eigenvalue problem From the geometric point of view, ``linear'' is synonymous with ``straight'', and consequently linear algebra can be regarded as the branch of mathematics dealing with lines and planes , as well as with transformations of space that preserve ``straightness'', e.g.

60. Introduction To Electronic Structure Calculations By Arkady V. Krasheninnikov. http://beam.acclab.helsinki.fi/~akrashen/esctmp.html

530018 Introduction to electronic structure calculations, 3 sw Description Lecturing time: Autumn 2002, Tuesday, 10-12, D106. Exercises: Wednesday 10-12, E206, every other week. First lecture: First exercise session: Lecturer: Dr. Arkady V. Krasheninnikov Extent of course: 3 sw, 6 ECTS credits Duration: 14 weeks Normal year to be taken: specialization phase, third year and up. Prerequisites: Introductory courses in quantum mechanics, solid-state physics, computational physics. Knowledge of the basics of Fortran or C programming languages. Language of instruction: English. The exercises and exam can be solved in English or German. The exam can be also solved in Finnish or Swedish by prior agreement. Course description: As a result of recent successes in describing and predicting properties of materials, electronic structure calculations have become increasingly important in the fields of physics and chemistry over the past decade, especially with the advent of present-day, high-performance computers. Assuming a knowledge of the types of atoms comprising any given material, a computational approach enables us to answer two basic questions: What is the atomic structure of the material and what are its electronic properties ? The methods used to derive answers to these questions will be the subject of the course. The student will be introduced to computational methods used in electronic structure calculations at various levels of sophistication: tight-binding approximation, density-functional theory, Hartree-Fock methods, etc. Lectures on concepts will be combined with practical exercises designed to enable the student not only to use the various standard codes, but also to develop new ones, if required. Special attention will be given to the electronic structure of nanosystems, such as carbon nanotubes and atomic clusters.

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