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. Ifn < 0
, the inverse is computed and then raised to theabs(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.]])