The following methods used to transform matrices: trading two rows, multiplying a row by a nonzero scalar, or adding a scalar multiple of one row to another row.
Page 1 of 5 RREFEtc.doc Winter 2007 Selected Definitions from http:/www.mathwo
Some Facts About Matrix Eigenvalues and Eigenvectors a. The eigenvalue problem is of the form Ax = x where the scalar is the eigenvalue and x is the (nonzero) eigenvector. b. If x is an eigenvector, then so is cx where c is any nonzero scalar.
c. A symmet
CEG/MTH/416/616 Matrix Computations Homework 1a Undergraduates: 5 points max Graduates: 5 points max Assigned: January 8, 2010 Due: January 12, 2010 Problem 1 (5 points) See Chapter 1 Datta 2nd edition handout page 5 given the first day of class. The E ma
CEG/MTH/416/616 Matrix Computations Homework Set # 2 - 20 max Assigned January 14, 2010. Due January 21, 2010
Problem 1 (20 points) Construct a matrix of zeros and ones of size 300 by 200. Call the matrix A. The use the MATLAB spy command: spy(A). The res
CEG/MTH/416/616 Matrix Computations Homework Set # 3 30 points max undergraduate 40 points max graduate Assigned January 26, 2010. Due February 2, 2010
Problem 1 (10 points) Study the Sherman-Morrison Formula (Datta, First Edition, page 239). (a) (5 point
CEG/MTH/416/616 Matrix Computations Homework Set # 4
Changes 2/21/10 see below.
50 points undergraduates and graduates. Assigned February 18, 2010. Due February 25, 2010. WebCT submittals of code.
Problem 1. (25 points) Modify the thomas.m code so that it
CEG/MTH/416/616 Matrix Computations Homework Set # 4 50 points undergraduates and graduates. Assigned February 18, 2010. of code. Due February 25, 2010. WebCT submittals
Problem 1. (25 points) Modify the thomas.m code so that it works with the columns of
Read and then Rewrite a Matrix Using Files
% tryreadwritefile.m clear; clc; % A row written 7 by 7 unsymmetical matrix is on file fid = fopen('umat.m','r'); disp('The data on the file is:'); type umat.m; [A,count] = fscanf(fid,'0',[7,7]); % Must transpose
CEG/MTH/416/616 Matrix Computations Winter 2010 Final Exam - Study Topics/Procedures General a. Review Mid-Term Exam and Quizzes: you may come by my office to discuss solutions. b. Review all your class notes c. Review text chapters covered d. Review Home
Page 1 of 1 2/2/2010 styexam1ceg416wi10.docx CEG/MTH/416/616 Winter 2010 CEG/MTH/416/416
MidExam - Study Topics/Procedures February 4, 2010 Study Topics Some topics listed will be covered in lecture on February 2, 2010 Study class notes. Study Datta t
Properties of Permutation Matrices
(last rev 4/28/03)
Let I denote the identity matrix of order n. Let P(r,s) be the I matrix of order n with rows r and s interchanged. The P(r,s) above is called an elementary permutation matrix. Let Pk = Pk(rk,sk) denote
Pivoted LU Factorization (Crout version)
Ref: (S&H) Applied Numerical Methods for Engineers, R. Schilling and S. Harris, Brooks/Cole, 2000. The purpose of these notes is to show how to compute the factors of a square matrix, A, of order n so that: (1) PA
MATH2071: LAB #12: The Eigenvalue Problem
TABLE OF CONTENTS
Introduction The Rayleigh Quotient The Power Method The Inverse Power Method Using Shifts The QR Method ASSIGNMENT
For any square matrix A, consider the equation det(A-lambda*I)=0.
CEG/MTH 416/616 End of Week 3 Online Documents for Study
Row Operations, Row Echelon Form and Related Topics http:/www.cs.wright.edu/~rtaylor/ceg416/other/content/LinearEqsEigNotes/RREFEtc.pdf
Properties of Permutation Matrices http:/www.cs.wright.edu/~rt
Solving Systems of Linear Equations by Cholesky Factorization Method Last Revised: November 5, 2002, by R. F. Taylor.
Ref: Numerical Analysis: Mathematics of Scientific computing, Third Edition, D. Kincaid and W. Cheney, Brooks/Cole, 2002, ISBN 0-53438905
;1 De nition 6.8.1 We shall call the number Cond(A x) = kjA kjjAjjxjk the Skeel's condition xk number and Conds(A) = kjA;1jjAjk the upper bound of the Skeel's condition number.
Cond(A x) is useful when the column norms of A;1 vary widely. Chandrasekaran a