In linear algebra, an orthogonal diagonalization of a symmetric matrix is a diagonalization by means of an orthogonal change of coordinates.[1]
The following is an orthogonal diagonalization algorithm that diagonalizes a quadratic form q(x) on Rn by means of an orthogonal change of coordinates X = PY.[2]
Then X=PY is the required orthogonal change of coordinates, and the diagonal entries of will be the eigenvalues which correspond to the columns of P.