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Random Problem Generator 1.5

Sang-gu Lee & Sunkyunkwan university Matrix Lab.

This is a self training system founded on the internet environment. In this system, you can improve your mathematical knowledge about the linear algebra. It will make a problem set which was generated randomly and you can intensify your  linear algebra skills by solving the problem set. If you passed elementary linear algebra classes, you can solve those problem-sets easily.

This system has been developed by the linear algebra team in Sungkyunkwan University. If you have any comments for this system, please contact us with your comments:
sglee@skku.edu

URL

http://galois09.skku.ac.kr/rpgs1.5/

FLASH Vector Grapher

Sang-gu Lee & Sunkyunkwan university Matrix Lab.

The example of multimedia education contents using FLASH and its development kit.

URL

http://matrix.skku.ac.kr/2009-Flash/vector2D_grapher2.htm

Java Matrix Calculator

Sang-gu Lee & Sunkyunkwan university Matrix Lab.

The example of multimedia education contents using Java and its development kit.

URL

http://matrix.skku.ac.kr/newMatrixCalENG11/Test.html

Linear Algebra with Cartoon

Sang-gu Lee & Sunkyunkwan university Matrix Lab.

The example of multimedia education contents using the cartoon.

URL

http://matrix.skku.ac.kr/ilas/er/module2/

Geschgorin Circle Theorem

Sang-gu Lee & Sunkyunkwan university Matrix Lab.

The example of multimedia education contents for the Geschgorin circle theorem and eigenvalue problem.

URL

http://matrix.skku.ac.kr/ilas/er/module1/

ATLAST

Project ATLAST has produced a variety of supplemental projects, exercise sets and MATLAB m-files for teaching matrix theory.

URL

http://www.umassd.edu/SpecialPrograms/Atlast/welcome.html

MATLAB in Education Web Page

URL

http://www.mathworks.com/academia/

Easing Eigenvalues and Eigenvectors into Introductory Linear Algebra

Abstract: We provide a series of exercises for a first linear algebra course that introduces the concepts of eigenvalue, eigenvector, and diagonalization. Using the simple, geometric idea of fixed vectors and fixed directions, the basic aspects of eigenvectors as multiplicative invariants of a matrix are emphasized. These exercises can be assigned as soon as students have learned about matrix multiplication, linear combinations of vectors, linear independence, and the solution of small linear systems.

URL

http://matrix.skku.ac.kr/ilas/er/er1.pdf

Eigenvalues, Eigenvectors, and Polynomials in a Matrix

Abstract: We provide further exercises for a first linear algebra course that develop the relationship between polynomials evaluated at a matrix, polynomials that annihilate a matrix, eigenvalues, and diagonalization. This is all done using the geometric concept of an eigenvector as a fixed direction for a matrix. These exercises are intended to follow the exercises in ''Easing into Eigenvectors and Eigenvalues in Introductory Linear Algebra''.

URL

http://matrix.skku.ac.kr/ilas/er/er2.pdf

Lessons Enhanced Using Technology

Summer, 1998

Abstract: Seven extended sample lessons that integrate various matrix software packages. These were written by various participants in the PCMI Undergraduate Faculty Program. There is also information on various types of software and technology in use in the teaching of undergraduate linear algebra.

URL

http://matrix.skku.ac.kr/ilas/er/data/rts.htm

Journal of Online Mathematics and its Applications

URL

[Link]

Materials for Linear Algebra

Click on a module name below to see an OVERVIEW of its contents.

Click on a helper application icon to FILTER the list below for modules that are available for use with a particular helper application.

modules at math.duke.edu

URL

http://www.math.duke.edu/education/ccp/materials/linalg/

Linear Algebra: Complete set of Lessons

URL

[Links]

Linear Algebra Toolkit - Main Page

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.

Przemyslaw Bogacki.
Department of Mathematics and Statistics
Old Dominion University
Norfolk, VA 23529
Phone: (757) 683-3262
E-mail: pbogacki@odu.edu

URL

http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi

mkaz.com : Mathematics : Linear Algebra

Matrix Calculator (Java Application) UPDATED: 2005-06-30
A Java application which lets you calculate the determinant, adjoint, inverse, transpose, and more of a 'n x n' matrix. (Source Code Available)

Linear Algebra Calculator (JavaScript)
A matrix calculator, which has the ability to calculate the determinant, adjoint, and inverse of a '3 x 3' matrix.

Linear System of 3 Equations (JavaScript)
A calculator that can solve a linear system of 3 equations and 3 unknowns, includes explanation on the mathematics behind it.

URL

http://mkaz.com/math/line_alg.html

Exploratories

The Exploratory Project is a research project of the Brown University Computer Graphics Research Group

URL

[Link1]

[Link2]

Interactive Data Fitting

You might like to experiment with this demo in order to evaluate the sensitivity of straight line fits to different types of data. For example, using the "Add Points" option provided, input several points that lie approximately along a line, and then observe that the LS and LAV fits are quite similar. Now move a point or two (thereby simulating data recording errors or the occurrence of "outlier" points), and note that the LAV fit is usually less influenced than the LS fit by these changes in the data. Statisticians refer to LAV fits as being more "robust" than LS fits, although they can provide deeper mathematical insight into LS fits in general.

Enjoy the demo, and please contact BCS by e-mail if you need assistance in solving challenging curve fitting problems.

URL

http://www.barrodale.com/java_demo/index.htm

Lights Out

URL

[Link1]

[Link2]

AN INTRODUCTION TO TOTAL LEAST SQUARES

This contains a tutorial paper written by Pieter de Groen. This paper provides an elementary introduction to Total Least Squares. There are two accompanying eps files for the paper: eps file 1a and eps file 1c. Pieter de Groen has written a textbook on Total Least Squares that has been published in 'Nieuw Archief', the journal of the Dutch Mathematical Society.

URL

http://matrix.skku.ac.kr/ilas/er/tasw1.pdf

Multilinear Algebra

Russ Merris has written a book entitled Multilinear Algebra. His description of the book is as follows: " Ideally suited for a fourth year undergraduate "capstone" course, Multilinear Algebra is also an attractive choice for a beginning graduate course and/or as a research reference. The first four chapters consist of self-contained introductions to those prerequisite notions beyond the standard third year undergraduate courses in abstract and linear algebra. Apart from applications to graph theory and the "excursion" into Invariant Theory, the use of Schur functions as a unifying vehicle in the final chapter may be of particular interest to combinatorialists." For the table of contents and purchase information.

URL

http://matrix.skku.ac.kr/ilas/er/merris_book.txt

Numerical Linear Algebra

Lloyd N. Trefethen and David Bau, III have recently written a text on numerical linear algebra. For review comments on the text, a description of the philosophy of the authors and their intended graduate level audience, and a detailed table of contents.

URL

http://matrix.skku.ac.kr/ilas/er/trefbau_book.txt