Orthogonal diagonalization

In linear algebra, an orthogonal diagonalization of a symmetric matrix is a diagonalization by means of an orthogonal change of coordinates. 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. The X=PY is the required orthogonal change of coordinates, and the diagonal entries of P T A P {displaystyle P^{T}AP} will be the eigenvalues λ 1 , … , λ n {displaystyle lambda _{1},dots ,lambda _{n}} which correspond to the columns of P.