sage: A = matrix(CDF, [[1, 2, 3], [4, 5, 6]]) sage: C = transpose(A)*A sage: P, L, U = C.LU() sage: P [0.0 0.0 1.0] [1.0 0.0 0.0] [0.0 1.0 0.0] sage: L [ 1.0 0.0 0.0] [ 0.62962962963 1.0 0.0] [0.814814814815 0.5 1.0] sage: U [ 27.0 36.0 45.0] [ 0.0 -0.666666666667 -1.33333333333] [ 0.0 0.0 -0.0] sage: L*U [27.0 36.0 45.0] [17.0 22.0 27.0] [22.0 29.0 36.0] sage: P*C [27.0 36.0 45.0] [17.0 22.0 27..