numpy.linalg.matrix_power¶

numpy.linalg.matrix_power(a,n)[source]¶

Raise a square matrix to the (integer) powern.

For positive integersn, the power is computed by repeated matrixsquarings and matrix multiplications. Ifn==0, the identity matrixof the same shape as M is returned. Ifn<0, the inverseis computed and then raised to theabs(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.
Returns:	a**n:(…, M, M) ndarray or matrix object The return value is the same shape and type asM;if the exponent is positive or zero then the type of theelements is the same as those ofM. If the exponent isnegative the elements are floating-point.
Raises:	LinAlgError For matrices that are not square or that (for negative powers) cannotbe inverted numerically.

Examples

>>>fromnumpy.linalgimportmatrix_power>>>i=np.array([[0,1],[-1,0]])# matrix equiv. of the imaginary unit>>>matrix_power(i,3)# should = -iarray([[ 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. elementsarray([[ 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 1array([[ 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.]])