numpy.linalg.matrix_power — NumPy v2.4 Manual (original) (raw)

linalg.matrix_power(a, n)[source]#

Raise a square matrix to the (integer) power n.

For positive integers n, the power is computed by repeated matrix squarings and matrix multiplications. If n == 0, the identity matrix of the same shape as M is returned. If n < 0, the inverse is computed and then raised to the abs(n).

Note

Stacks of object matrices are not currently supported.

Parameters:

a(…, M, M) array_like

Matrix to be “powered”.

nint

The exponent can be any integer or long integer, positive, negative, or zero.

Returns:

a**n(…, M, M) ndarray or matrix object

The return value is the same shape and type as M; if the exponent is positive or zero then the type of the elements is the same as those of M. If the exponent is negative the elements are floating-point.

Raises:

LinAlgError

For matrices that are not square or that (for negative powers) cannot be inverted numerically.

Examples

import numpy as np from numpy.linalg import matrix_power i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit matrix_power(i, 3) # should = -i array([[ 0, -1], [ 1, 0]]) matrix_power(i, 0) array([[1, 0], [0, 1]]) matrix_power(i, -3) # should = 1/(-i) = i, but w/ f.p. elements array([[ 0., 1.], [-1., 0.]])

Somewhat more sophisticated example

q = np.zeros((4, 4)) q[0:2, 0:2] = -i q[2:4, 2:4] = i q # one of the three quaternion units not equal to 1 array([[ 0., -1., 0., 0.], [ 1., 0., 0., 0.], [ 0., 0., 0., 1.], [ 0., 0., -1., 0.]]) matrix_power(q, 2) # = -np.eye(4) array([[-1., 0., 0., 0.], [ 0., -1., 0., 0.], [ 0., 0., -1., 0.], [ 0., 0., 0., -1.]])