Raise a square matrix to the power n in Linear Algebra in Python

To raise a square matrix to the power n in Linear Algebra, use the numpy.linalg.matrix_power() in Python 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).

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. The 1st parameter, a is a matrix to be “powered”. The 2nd parameter, n is the exponent that can be any integer or long integer, positive, negative, or zero.

Steps

At first, import the required libraries −

import numpy as np
from numpy.linalg import matrix_power

Create a 2D array, matrix equivalent of the imaginary unit −

arr = np.array([[0, 1], [-1, 0]])

Display the array −

print("Our Array...\n",arr)

Check the Dimensions −

print("\nDimensions of our Array...\n",arr.ndim)

Get the Datatype −

print("\nDatatype of our Array object...\n",arr.dtype)

Get the Shape −

print("\nShape of our Array object...\n",arr.shape)

To raise a square matrix to the power n in Linear Algebra, use the numpy.linalg.matrix_power() in Python. 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) −

print("\nResult...\n",matrix_power(arr, 0))

Example

import numpy as np
from numpy.linalg import matrix_power

# Create a 2D array, matrix equivalent of the imaginary unit
arr = np.array([[0, 1], [-1, 0]])

# Display the array
print("Our Array...\n",arr)

# Check the Dimensions
print("\nDimensions of our Array...\n",arr.ndim)

# Get the Datatype
print("\nDatatype of our Array object...\n",arr.dtype)

# Get the Shape
print("\nShape of our Array object...\n",arr.shape)

# To raise a square matrix to the power n in Linear Algebra, use the numpy.linalg.matrix_power() in Python
print("\nResult...\n",matrix_power(arr, 0))

Output

Our Array...
[[ 0 1]
[-1 0]]

Dimensions of our Array...
2

Datatype of our Array object...
int64

Shape of our Array object...
(2, 2)

Result...
[[1 0]
[0 1]]