matrix_power(a, 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

a : (..., M, M) array_like

Matrix to be "powered".

n : int

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

Raises

LinAlgError

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

Returns

a**n : (..., M, M) ndarray or matrix object

The return value is the same shape and type as :None:None:`M`; if the exponent is positive or zero then the type of the elements is the same as those of :None:None:`M`. If the exponent is negative the elements are floating-point.

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

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.]])

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

dask.array.ufunc.square

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