Matrices I&II (Math7370-7380)
Goal: This course gives a
mathematically rigorous treatment of matrices and surveys modern approaches
and advances in matrix theory.
Text: Matrix Analysis, by R. A. Horn and C.R. Johnson, Cambridge University Press, 1990.
The 2nd edition (2012) just came out. Amazon has a Kindle version and Barnes & Noble has a Nook version. Professor Roger A. Horn (email@example.com) would be glad to receive typos or errors from you so he can update the Errata
Math 7370: Chapter 1-4 plus some supplmentary materials
Math 7380: Chapter 5-8 plus some supplementary materials
Reference: Topics in Matrix Analysis, by R. A. Horn and C. R. Johnson, Cambridge University Press, 1991.
Basic reference for linear algebra and linear maps: Finite-Dimensional Vector Spaces, by Paul R. Halmos, Springer, 1974.
Grades are determined by homework (50%) and 2 tests (50%). Test 1 will be given in mid Oct and Test 2 will be given in early December.
There is no final examination.
Homeworks (based on the 1990 edition of Horn and Johnson):
Chapter 1: Homework 1 (1.1 #2,3,5,8); Homework 2 (1.2 #2,4,6; 1.3 #4,5,8); Homework 3 (1.4 #1, 4, 5, 10, A1. Show by induction that each nxn complex matrix is similar to an upper triangular matrix. A2. Show that any commuting family of nxn complex matrices is simultaneously triangularizable) (Key on Exercises) (Key on Problems)6.1 #2,7,10; 6.2 #1,3; (Key on Exercises) (Key on Problems) Chapter 7: Homework 5: 7.1 #2, 4; 7.2 #3, 8; Homework 6: 7.3 #4, 5, 11, 13, 19; (Key on Exercises) (Key on Problems) Chapter 8: Homework 7: 8.1 #1,4; 8.2 #1, 7-9; Homework 8: 8.3 #1,6,8; 8.4 #5,6; (Key on Exercises) (Key on Problems)
Journals publishing linear algebra/matrices:
Journal of Linear Algebra and Its Applications
Journal of Linear and Multilinear Algebra
Electronic Linear Algebra
Operators and Matrices