Matrices I&II (Math7370-7380)
Goal: This course gives a
mathematically rigorous treatment of matrices and surveys modern approaches
and advances in matrix theory.
Outline of Content:
Math7370,
Math7380
Text: (Math 7370) Matrix Analysis, by R. A. Horn and C.R. Johnson, Cambridge University Press, 1990.
(Chapter 1-4 plus some supplmentary materials)
(Math 7380) Matrix Analysis, by R. A. Horn and C.R. Johnson, Cambridge University Press, 1990. (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.
Lectures: Parker 322, 11:00-12:15 pm. (TR) Office hours: 9:00-11:00am (TR)
Grades:
Grades are determined by the performance of tests (1/2) and quizzes (1/2).
There is no final examination.
Homeworks:
Chapter 1: 1.0 #1-2; 1.1 #1-8; 1.2 #1-10; 1.3 #1-8,10, 12-16 (do #15 before #5); 1.4 #1-10 (assume A nonsingular and the last A should be the inverse of A) (Solutions and remarks on Chapter 1)
Chapter 2: 2.1 #1-14; 2.2 #1-5, 8; 2.3 #1-8; 2.4 #1-2, 4-14; 2.5 #3-5, 8-10, 12-16 25-28; 2.6 #3-5 (Solutions and remarks on Chapter 2)
Chapter 3: 3.1 #1; 3.2 #1-13, 16-17; 3.3 #1-4, 7-16; 3.4 #1-4; 3.5 1-6 (Solutions and remarks on Chapter 3)
Chapter 4: 4.1 #1-4, 6-14; 4.2 #1-5; 4.3; 5-7, 9-11, 13-17 (Solutions and remarks on Chapter 4)Key: Quiz 1, Quiz 2, Test 1, Quiz 3, Quiz 4, Quiz 5, Test 2, Quiz 6, Quiz 7, Test 3, Quiz 8, Test 4
Chapter 5: 5.1 #1, 3-9; 5.2 #4,6-9 5.3 #1-2; 5.4 #1, 3, 7-12; 5.5 #7, 9; 5.6 #1-3, 5, 7, 10, 12-13, 15-16, 19-21, 37 (Solutions and remarks on Chapter 5)
Chapter 6: 6.1 #2, 5-11; 6.2 #1-4; (Solutions and remarks on Chapter 6) Chapter 7: 7.1 #1-6; 7.2 #1-4, 8-9, 11; 7.3 #1-5,11, 13, 19; 7.8 #3, 7-10, 13 (Solutions and remarks on Chapter 7) Chapter 8: 8.1 #1-7; 8.2 #1, 5-9; 8.3 #1-6,8; 8.4 #1-16; (Solutions and remarks on Chapter 8)Key: Quiz 1, Quiz 2, Quiz 3, Test 1, Quiz 4, Quiz 5, Test 2, Quiz 6, Quiz 7, Test 3, Quiz 8, Quiz 9, Test 4
Journals publishing linear
algebra/matrices:
Journal of Linear Algebra and Its Applications
Journal of Linear and Multilinear Algebra