# Math 430/630 - Matrix Analysis

## Basic Information

• Matthias K. Gobbert, Math/Psyc 416, (410) 455-2404, gobbert@math.umbc.edu,
office hours: TTh 04:00-05:00 or by appointment
• Lectures: TTh 05:30-06:45, MP 401; see the schedule for more information.
• Prerequisites: Math 251, Math 301, CMSC 201, or instructor approval
• Copies of all following books are on reserve in the library.
• Required textbook: Lloyd N. Trefethen and David Bau, III, Numerical Linear Algebra, SIAM, 1997 and 2000. Notice that the bookstore may stock the book under Math 430. Note: SIAM has published both a softcover (1997) and a hardcover (2000) version of this book; they are identical in content, and you may use either one of them.
• Recommended book on Iterative Methods: David S. Watkins, Fundamentals of Matrix Computations, second edition, Wiley, 2002.
• Recommended book on Matlab: Desmond J. Higham and Nicholas J. Higham, Matlab Guide, SIAM, 2000. Webpage of the book including list of errors.
 Homework Presentations Project Midterm Final 30% 10% 10% 20% 30%
The homework is weighted so heavily, because it includes the computer assignments that are vital to understanding the course material. The presentations consist of presenting selected homework problems in class on the board; I will assign the problems to individual students throughout the semester. Both Math 430 and 630 will have projects with professional grade type-set reports, but they will be different in level; they will be assigned as early as possible and are due before the end of classes. See also the general policies and procedures for more information.

## Overview

Matrix Analysis encompasses the theory of matrices as well as the practice of using numerical methods to implement the associated algorithms in a computer. The most classical example of a computational technique that is used both for hand calculations as well as in the computer is Gaussian elimination to find the solution to a linear system of equations; a version of this algorithm is known as reduction to row echelon form. Starting with knowledge from basic linear algebra, we will build up familiarity with advanced concepts and their application.

The course will start by introducing basic definitions like vector and matrix norms and the singular value decomposition. In addition to linear system of equations, we will study least-squares problems and eigenvalue computations, and various numerical methods to solve them. Those methods include both direct methods (that produce the solution in a fixed number of steps) and iterative methods (that get closer to the solution the more steps are taken). We will discuss advantages and drawbacks of both types of methods, based both on theoretical considerations and implementation details.

Instructions: Open the file by clicking on the link; plain text should appear in your browser window. Then use the ``File -> Save As'' functionality of your browser to save the data to a file. Or use the right mouse button to directly save the file without opening it first. The details may vary depending on your browser software and operating system. Contact me if there is a persisting problem.

#### Project:

• setupA.m Matlab function for setup of system matrix

## Official UMBC Honors Code

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