# cirq.diagonalize_real_symmetric_and_sorted_diagonal_matrices¶

cirq.diagonalize_real_symmetric_and_sorted_diagonal_matrices(symmetric_matrix: numpy.ndarray, diagonal_matrix: numpy.ndarray, tolerance: cirq.linalg.tolerance.Tolerance = Tolerance(rtol=1e-05, atol=1e-08, equal_nan=False)) → numpy.ndarray[source]

Returns an orthogonal matrix that diagonalizes both given matrices.

The given matrices must commute.
Guarantees that the sorted diagonal matrix is not permuted by the
diagonalization (except for nearly-equal values).
Parameters: symmetric_matrix – A real symmetric matrix. diagonal_matrix – A real diagonal matrix with entries along the diagonal sorted into descending order. tolerance – Numeric error thresholds. An orthogonal matrix P such that P.T @ symmetric_matrix @ P is diagonal and P.T @ diagonal_matrix @ P = diagonal_matrix (up to tolerance). ValueError – Matrices don’t meet preconditions (e.g. not symmetric). ArithmeticError – Failed to meet specified tolerance.