Positive Definite Matrices eigenvalues

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Main Question or Discussion Point

[SOLVED] Positive Definite Matrices

a) If A is Symmetric show that A-λI is positive definite if and only if all eigenvalues of A are >λ, and A-λI is negative definite if and only if all eigenvalues of A are <λ.

b) Use this result to show that all the eigenvalues of
[ 5 2 -1 0]
[ 2 5 0 1]
[-1 0 5 -2]
[ 0 1 -2 5]
are between zero and eight.
 

Answers and Replies

HallsofIvy
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Didn't you read the files you were asked to when you registered?

You have now posted three consecutive questions (which look like homework and so should have been posted in the homework sections) without showing any work or any attermpt at a solution by yourself. You are required to show what you have done so we will know what kind of help you need.
 
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So I made a mistake, and I figured it out. It's not like I can delete them. I have already posted to homework, and gotten it solved. Thanks though.
 

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