dpnp.linalg.matrix_power

dpnp.linalg.matrix_power(a, n)

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

For full documentation refer to numpy.linalg.matrix_power.

Parameters:

• a ((..., M, M) {dpnp.ndarray, usm_ndarray}) – Matrix to be “powered”.

• n (int) – The exponent can be any integer or long integer, positive, negative, or zero.

Returns:

• a**n ((…, M, M) dpnp.ndarray) – 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.

• >>> import dpnp as np

• >>> i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit

• >>> np.linalg.matrix_power(i, 3) # should = -i

• array([[ 0, -1], – [ 1, 0]])

• >>> np.linalg.matrix_power(i, 0)

• array([[1, 0], – [0, 1]])

• >>> np.linalg.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.]])

• >>> np.linalg.matrix_power(q, 2) # = -np.eye(4)

• array([[-1., 0., 0., 0.], – [ 0., -1., 0., 0.], [ 0., 0., -1., 0.], [ 0., 0., 0., -1.]])