Orthogonal diagonalization of a real square matrix 
is a factorization
 |
where 
is an orthogonal matrix and 
is a diagonal matrix. The
columns of 
form an orthonormal eigenbasis of 
, and the diagonal entries of 
are the corresponding eigenvalues.
A real matrix is orthogonally diagonalizable iff
it is symmetric. The complex analogue replaces
orthogonal matrices and transposition
by unitary matrices and conjugate
transposition; precisely the normal matrices
are unitarily diagonalizable.
