Math 2406: Abstract Vector Spaces
Lecture 23 Plan
(Tuesday, November 13
Apostol 6.15-6.16.
Today we'll finish Chapter 6 by discussing the Jordan Normal Form of a matrix, and then do some exercises on eigenvalues and eigenvectors. The Jordan normal form tells one the eigenvalues of matrix, and how many eigenvectors it has.
Review questions:
1. How many eigenvectors does
the matrix A in exercise 9.h, P. 208, have? What are the eigenvalues?
2. Say a matrix A is n-by-n. What are the possible numbers of
eigenvectors for A to have?
Office hours this week: Weds.
4-5 p.m., Fri. 3-5 p.m. (to go over Test 2 review problems, see below).
NOTE: I will not be here on
Monday 11/19 or Tuesday 11/20.
Test 2 Review problems (Not to
be handed in):
4.16 #8, 11, 14; 4.20 #5, 11, 15; 4.21 #4, 5, 9; 5.8 #1, 3, 4, 7, 9;
5.15 #2, 6, 7; 6.4 # 1,3, 4; 6.10 #6,7, 11.