Transcript MAT1225 - Seattle Pacific University

MAT 2401
Linear Algebra
7.2 Diagonalization
http://myhome.spu.edu/lauw
HW
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WebAssign 7.2
Tomorrow…
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

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.
Preview
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How to compute the power of a matrix
by using eigenvalues and eigenvectors.
The Problem
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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).
The Special Case
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If D is a diagonal matrix, Dk is easy to
compute.
1
0
D


0

0
2
0

0


 0
k
, D  
0



n 
 0

0
0
0 



0 



The no. of multiplication for each
matrix multiplication is ________
How to Take the Advantage?
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If we can write A as PDP-1 for some
matrices P and D, then …
A k=
How to Find P and D?
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.