10/2/2008

Discussion of Exam

• You will be allowed to use one 8.5" x 11" note sheet during the exam.
• The exam will consist of two parts, one with Maple and one without Maple

Problem Session

Coordinates in a subspace of R^n

Linearity of Coordinates

The matrix of a linear transformation

Standard matrix versus B-matrix

Similar Matrices

• Consider two n x n matrices A and B. We say that A is similar to B if there exists an invertible matrix S such that AS = SB, or B = S^(-1)AS.

Similarity is an equivalence relation

• An n x n matrix A is similar to itself (reflexitivity).
• If A is similar to B, then B is similar to A (symmetry).
• If A is similar to B and B is similar to C, then A is similar to C (transitivity).

Group/Class Exercises

• Section 3.4 - 4, 6, 10, 18, 23, 60

Good luck with your preparation for Exam 1.