# numpy.linalg.matrix_power¶

numpy.linalg.matrix_power(M, n)

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).

Parameters : M : ndarray or matrix object Matrix to be “powered.” Must be square, i.e. M.shape == (m, m), with m a positive integer. n : int The exponent can be any integer or long integer, positive, negative, or zero. M**n : 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. LinAlgError : If the matrix is not numerically invertible.

matrix
Provides an equivalent function as the exponentiation operator (**, not ^).

Examples

```>>> from numpy import linalg as LA
>>> i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit
>>> LA.matrix_power(i, 3) # should = -i
array([[ 0, -1],
[ 1,  0]])
>>> LA.matrix_power(np.matrix(i), 3) # matrix arg returns matrix
matrix([[ 0, -1],
[ 1,  0]])
>>> LA.matrix_power(i, 0)
array([[1, 0],
[0, 1]])
>>> LA.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 quarternion units not equal to 1
array([[ 0., -1.,  0.,  0.],
[ 1.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  1.],
[ 0.,  0., -1.,  0.]])
>>> LA.matrix_power(q, 2) # = -np.eye(4)
array([[-1.,  0.,  0.,  0.],
[ 0., -1.,  0.,  0.],
[ 0.,  0., -1.,  0.],
[ 0.,  0.,  0., -1.]])
```

numpy.einsum

numpy.kron