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This is a T/F question:

all symmetric matrices are diagonalizable.

I want to say no, but I do not know how exactly to show that.... all I know is that to be diagonalizable, matrix should have enough eigenvectors, but does multiplicity of eigenvalues matter, i.e. can I say that if eignvalue has multiplicity > 1 then the matrix is not diagonalizable?

Thanks

EDIT: zero matrix is diagonalizable, right?

all symmetric matrices are diagonalizable.

I want to say no, but I do not know how exactly to show that.... all I know is that to be diagonalizable, matrix should have enough eigenvectors, but does multiplicity of eigenvalues matter, i.e. can I say that if eignvalue has multiplicity > 1 then the matrix is not diagonalizable?

Thanks

EDIT: zero matrix is diagonalizable, right?

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