1 unitary, if complex eigenvalues are involved
2 Similar result for complex matrices: A Hermitian matrix has all real eigenvalues and is diagonalizable through a unitary similarity transformation.
3 There is a typical mistake committed by some confused beginners in examinations. In response to the problem— “Diagonalize the following matrix: ⋯. ”, they end up running a full Gauss-Jordan elimination, ‘obtaining’ a diagonal matrix at the end, giving rise to an awkward situation. Indeed, this error is more semantic than mathematical. Nevertheless, the author would urge the reader to refrain from this blunder.