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MATH462: Linear Algebra
Revised: November 2006
Course Description
Rigorous treatment of topics from linear algebra including algebra of linear transformation, dual space, algebra of polynomials, determinants, eigenvalues, diagonalization, and selected applications. Prerequisite: Math 362. Three semester hours.
Objectives
-
To expose the student to some relatively deep theorems in linear algebra.
- To further develop the student's ability to reason abstractly.
Text
Roger Horn and Charles Johnson, Matrix Analysis, 1985 (reprinted in 1999), Cambridge University Press.
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Course Outline
Chapter 0: Review and Miscellanea
Key topics of review from Math362 as well as generalizations and some advanced material. Topics include generalized vector spaces, determinants, nonsingularity, the usual inner product, the Gram-Schmidt process, and change-of-basis matrices. (The instructor should be selective of the material covered in this chapter, and allow this chapter to serve as a "reference section.") 10 days.Chapter 1: Eigenvectors, Eigenvalues, and Similarity
The eigenvector-eigenvalue equation, the characteristic polynomial, similarity (and diagonalization), and eigenvectors. 12 days.Chapter 2: Unitary Equivalence and Normal Matrices
Unitary matrices, unitary equivalence, Schur.s theorem, normal matrices, and the QR factorization. 8 days.Other topics as time allows.
Suggested topics are: The Jordan canonical form and the minimal polynomial (from Chapter 3), vector and matrix norms (from Chapter 5), the singular value decomposition, and LU factorization. 8 days.- Note: At appropriate places in this course, time should be allotted to elaborate on the historical aspects relevant to the subject.