In linear algebra, an orthogonal diagonalization of a normal matrix (e.g. 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 n 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.
In linear algebra, an orthogonal diagonalization of a normal matrix (e.g. 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 n 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.