Repeated eigenvalues of a symmetric matrix


by matqkks
Tags: eigenvalues, linear alegbra
matqkks
matqkks is offline
#1
Dec21-12, 04:17 PM
P: 150
I have been trying to prove the following result:
If A is real symmetric matrix with an eigenvalue lambda of multiplicity m then lambda has m linearly independent e.vectors.
Is there a simple proof of this result?
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Robert1986
Robert1986 is offline
#2
Dec21-12, 05:15 PM
P: 828
Do you know that symmetric matrices can be (orthogonally) diaganalised?
matqkks
matqkks is offline
#3
Dec22-12, 04:54 AM
P: 150
Quote Quote by Robert1986 View Post
Do you know that symmetric matrices can be (orthogonally) diaganalised?
That is the result I am trying to prove. Just need to show the result for repeated eigenvalue.


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