# Proof problem(Linear Algebra- Eigenvalues/Eigenvectors)

## Homework Statement

True/False
The geometric multiplicity of an eigenvalue of a symmetric matrix necessarily equals to its algebric multiplicity.

## The Attempt at a Solution

True.
If a matrix is symmetric, then the matrix is diagonalizable. Since the matrix is diagonalizable, there must be eigenvectors correspond to each eigenvalues.

So, I did the proof, but I'm not so sure if it sounds right. I think there could be something more tricky or missing. Would you guys check if this sounds right to you?

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Dick
Homework Helper
Sound right to me.

Thanks for checking. Just quick checking tho,
'A matrix is symmetric if and only if the matrix is diagonalizable.'

Is this a right statement?

or 'orthogonally diagonalizable'

Dick
Homework Helper
Thanks for checking. Just quick checking tho,
'A matrix is symmetric if and only if the matrix is diagonalizable.'

Is this a right statement?

or 'orthogonally diagonalizable'
No, it's not iff. Is the matrix [[1,1],[0,0]] diagonalizable? Is it symmetric?

oh, thanks!

Dick