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## Homework Statement

True/False

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

## Homework Equations

## 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?