(a)
Yes. A real symmetric matrix can be (orthogonally diagonalised).
(b)
No. This is a rotation matrix. The eigenvalues are non-real except for special values of .
(a)
Yes. A real symmetric matrix can be (orthogonally diagonalised).
(b)
No. This is a rotation matrix. The eigenvalues are non-real except for special values of .