1. MAT 2401 Linear Algebra
7.2 Diagonalization

2. HW
WebAssign 7.2

3. Tomorrow… Make sure you come to class tomorrow.
We will talk about the final exam.
We will also talk about the possibility of opting out from the final exam.

4. Preview
How to compute the power of a matrix by using eigenvalues and eigenvectors.

5. The Problem
Many applications involve the computation of the power of a matrix, Ak .
The process is very computational expensive. (n3 multiplications for a nxn matrix for each matrix multiplication).

6. The Special Case If D is a diagonal matrix, Dk is easy to compute.
The no. of multiplication for each matrix multiplication is ________

7. How to Take the Advantage?
If we can write A as PDP-1 for some matrices P and D, then …
Ak=

8. How to Find P and D?

9. Lab
Given a 2x2 matrix A. 1. Compute A6 by hand. 2. Use eigenvalues and eigenvectors to find A6. Warning: Do not use any calculating devices.