# numpy.linalg.matrix_power#

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

```>>> 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.]])
```