Repeated eigenvalues of a symmetric matrix

matqkks
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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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Do you know that symmetric matrices can be (orthogonally) diaganalised?
 
Robert1986 said:
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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