In linear algebra, an orthogonal diagonalization of a symmetric matrix is a diagonalization by means of an orthogonal change of coordinates. 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. 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.
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