MATH 261-01, Linear Algebra, Spring 2013

Abstract

Linear algebra is a subject of great theoretical and practical importance. It has been aptly described as the workhorse of mathematics. It is used in many branches of mathematics, including analysis, algebra, combinatorics, and geometry. It also has applications to biology, physics, economics, computer science, and other disciplines. We will focus on the theoretical aspects of the subject, though if time permits, we may explore one or more special topics such as the singular value decomposition, linear programming, or an application to biology or physics. We will cover most of Chapters 1 through 6 and of Chapter 8 of your text. I may skip some sections or ask you to read them on your own in order to ensure that we have adequate time to cover certain important topics that occur towards the end of the semester. Some of the main themes we will discuss include systems of linear equations and Gauss-Jordan elimination, vectors, matrices and matrix algebra, the notion of dimension, the connection between matrices and an important class of functions called linear transformations, determinants, eigenvalues and eigenvectors, and an important operation called diagonalization that can sometimes be performed on matrices.