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.
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:
Grades are determined by the performance of homework and classroom performance.
There is no final examination.
Homeworks:
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)
Chapter 2: Homework 4 (2.1 #9, 14, 2.2 #3, 4); Homework 5 (2.3 #1, 6 2.4 #4, 9); Homework 6 (2.5 #1, 8 2.6 #3) (Key on Exercises) (Key on Problems)
Chapter 3: Homework 7 (3.2 #2, 7, 8); Homework 8 ( 3.3 #3, 4, 9); Homework 9 (3.4 #4 3.5 #3, 6) (Key on Exercises) (Key on Problems)
Chapter 4: Homework 10 (4.1 #6, 11, 15); Homework 11 (4.2 #1, 2, 5); Homework 12 (4.3 #9, 11, 16) (Key on Exercises) (Key on Problems)
Chapter 5: Homework 1: 5.1 #5, 8, 9; 5.2 #4; Homework 2: 5.4 #3,7,9; 5.5 #7, 9; Homework 3: 5.6 #7,19,21 (Key on Exercises) (Key on Problems)
Chapter 6: Homework 4: 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