linalg.matrix_power

Description

For positive integer 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 of a matrix is computed and then raised to the power of abs(n).

Mandatory Input Parameters

Parameter	Type	Description
a	(…,M,M) array_like	Matrix to be "powered"
n	int	The exponent can be any integer or long integer, positive, negative, or zero.

Optional Input Parameters

None

Return Value

Type	Description
(…, M, M) ndarray or matrix object	The shape and type of the return value are the same as those of M. If the exponent is positive or zero, the type of the elements is the same as that of M. If the exponent is negative, the elements are floating-point.

Type

Description

(…, M, M) ndarray or matrix object

The shape and type of the return value are the same as those of M.

If the exponent is positive or zero, the type of the elements is the same as that of M.
If the exponent is negative, the elements are floating-point.

Examples

>>> import numpy as np
>>> a = np.array([[0,1], [-1,0]])
>>> np.linalg.matrix_power(a, 3)
array([[ 0, -1],
       [ 1,  0]])
>>> 
>>> np.linalg.matrix_power(a, 0)
array([[1, 0],
       [0, 1]])
>>> 
>>> np.linalg.matrix_power(a, -3)
array([[ 0.,  1.],
       [-1.,  0.]])
>>> 
>>> q = np.zeros((4,4))
>>> q[0:2, 0:2] = -a
>>> q[2:4, 2:4] = a
>>> a
array([[ 0,  1],
       [-1,  0]])
>>> 
>>> np.linalg.matrix_power(q, 2)
array([[-1.,  0.,  0.,  0.],
       [ 0., -1.,  0.,  0.],
       [ 0.,  0., -1.,  0.],
       [ 0.,  0.,  0., -1.]])
>>>

Parent topic: Linear Algebra Functions