Math 550 Linear Algebra and Applications
1
Revised 8/08/07
Notes on MATLAB Assignments
These notes are written to introduce the MATLAB part of this course. For additional MATLAB tutorial
materials, go to the course web site math.rutgers.edu/courses/550A a

Math 642:550 Summer 2008 MTTh 6:008:30 PM Hill 425 Prof. Bumby
Supplement 5, Matrix Exponentials
1. Introduction
It is now common for textbooks for a rst course in Differential Equations to describe the solution of the rst-order, linear, constant-coefcien

Math 642:550 Summer 2008 MTTh 6:008:30 PM Hill 425 Prof. Bumby
Supplement 4, Finding eigenvectors
1. Introduction Important theoretical results are that: (1) eigenvalues are characterized as the roots of the characteristic polynomial ; and (2) the charact

Math 642:550 Summer 2008 MTTh 6:008:30 PM Hill 425 Prof. Bumby
Supplement 3, The Cauchy-Binet formula
1. Introduction
The theorem that the determinant of a product of square matrices is the product of the determinants of the factors is so memorable that o

Math 642:550 Summer 2008 MTTh 6:008:30 PM Hill 425 Prof. Bumby
Supplement 2, The sign of a permutation
1. Introduction
Proofs will not play a large role in this course. However, any calculation (and, even more so, any program that will be used to perform

Math 642:550 Summer 2008 MTTh 6:008:30 PM Hill 425 Prof. Bumby
Supplement 1, Prerequisites
1. Introduction
A motivation for the subject of Linear Algebra is to organize the techniques for solving systems of linear equations. Since you should have had a co

Computing the Jordan Canonical Form Let A be an n by n square matrix. If its characteristic equation A (t) = 0 has a repeated root then A may not be diagonalizable, so we need the Jordan Canonical Form. Suppose is an eigenvalue of A, with multiplicity r a

Math 550A
MATLAB Assignment #5
1
Revised 12/11/13
LAB 5: Positive-Denite Matrices, Cholesky Factorization,
Singular Value Decomposition, and Digital Image Processing
In this lab you will use Matlab to study the following topics:
Tests for positive-denite

Review problems for Final Exam in 642:550 in Fall 2014
These problems are taken from past nal exams and problems in the text. The nal
exam will be similar in form to this collection of problems. The nal covers problems from
the entire semester.
1 1
A = 1

Math 642:550 Summer 2008 MTTh 6:008:30 PM Hill 425 Prof. Bumby
Supplement 6, Schurs unitary triangularization theorem.
1. Introduction
Section 5.6 of the text attempts to explain the signicance of the similarity between matrices A and B given by the equat

Math 642:550 Summer 2008 MTTh 6:008:30 PM Hill 425 Prof. Bumby
Supplement 7, The Perron-Frobenius Theorem.
Introduction Square matrices whose entries are all nonnegative have special properties. This was mentioned briey in Section 5.3 with a sketch of the

Math 642:550 Summer 2008 MTTh 6:008:30 PM Hill 425 Prof. Bumby
Supplement 8, The Pseudoinverse
1. Introduction
The text uses the Singular Value Decomposition to describe the pseudoinverse, since it gives an easy proof of existence, but it is not necessary

Finite Fourier Transform, Circulant Matrices,
and the Fast Fourier Transform
Roe Goodman
Supplementary Class Notes for Math 642:550 Linear Algebra and Applications
Rutgers, The State University of New Jersey
Revised March 3, 2013
1
Sampling and Aliasing
S

Math 550A
MATLAB Assignment #1
1
Revised 9/22/10
LAB 1: Gaussian Elimination, LU Factorization, and Solving Ax = b
In this lab you will use Matlab to study the following topics:
Gaussian elimination and reduced row echelon form of a matrix.
The LU (lowe

Math 550A
1
MATLAB Assignment #2
Revised 8/14/10
LAB 2: Orthogonal Projections, the Four Fundamental Subspaces,
QR Factorization, and Inconsistent Linear Systems
In this lab you will use Matlab to study the following topics:
Geometric aspects of vectors:

Math 550A
MATLAB Assignment #3
1
Revised 8/14/10
LAB 3: Determinants, Eigenvalues, and Eigenvectors
In this lab you will use Matlab to study the following topics:
The determinant function: its properties and how it is calculated from the P A = LU matrix

Math 550A
1
MATLAB Assignment #4
Revised 8/23/10
LAB 4: Unitary Diagonalization of Matrices, QR Algorithm,
Finite Fourier Transform, and Fast Fourier Transform
In this lab you will use Matlab to study the following topics:
Diagonalization of hermitian an

Math 550A
MATLAB Assignment #5
1
Revised 12/11/12
LAB 5: Positive-Denite Matrices, Cholesky Factorization,
Singular Value Decomposition, and Digital Image Processing
In this lab you will use Matlab to study the following topics:
Tests for positive-denite

Math 642:550 Summer 2008 MTTh 6:008:30 PM Hill 425 Prof. Bumby
Supplement 10, Numerical Methods in Linear Algebra
1. Introduction
Chapter 7 of the textbook describes computer algorithms for solving equations and nding eigenvalues and eigenvectors. Numeric

Math 642:550 Summer 2008 MTTh 6:008:30 PM Hill 425 Prof. Bumby
Supplement 9, A robust method for nding characteristic polynomials
It is easy to read too much into the denition of the characteristic polynomial as a determinant. As soon as the n by n matrix

642:550 Applied Linear Algebra
Fall 2004
Page 1
A Review Sheet for the Final Exam 12/20/2004
Here are some examples of problems you should be able to do on the nal. Other examples of problems can be found in the review sheet for the midterm and the answer