I know that
Hermitian matrices are always diagonalizable and real symmetric matrices are real Hermitian matrices and therefore diagonalizable.
But, it is always not the case that a symmetric matrix is a Hermitian matrix.
So my question is I think every real symmetric matrix is diagonalizable, but is it true for every symmetric matrix?
$1$ and $-1$ are only possible eigenvalues for real orthogonal matrix?