Numpy linalg.matrix_rank() is used to calculate the power n of a square matrix. What does that mean is that if we have a square matrix M and we have an integer n, then this function is used to calculate Mn?
Numpy linalg matrix_power()
To calculate the power of matrix m, use the np matrix_power() function. The matrix_power() method raises a square matrix to the (integer) power n.
If the value of n=0, then it calculates on the same matrix, and if the value of is n<0, then this function first inverts the matrix and then calculates the power of abs(n).
Syntax
numpy.linalg.matrix_power(M,n)
Parameters
The matrix_power() function takes two parameters:
- M: This is the square matrix on which we want to operate.
- n: This is the power value of the matrix.
Return Value
The method returns an integer after calculating the power.
Programming example
Program when the value of N is greater than 0
# Program when the value of N is greater than 0
from numpy import linalg as LA
import numpy as np
arr1 = np.array([[1, 2, 3], [3, 2, 4], [1, 0, 1]])
print("The array is:\n", arr1)
# When n=2
print("Matrix Power is:\n", LA.matrix_power(arr1, 2))
arr2 = np.array([[1, 2], [2, 1]])
print("The array is:\n", arr2)
# When n=1
print("Matrix Power is:\n", LA.matrix_power(arr2, 1))
Output
The array is: [[1 2 3] [3 2 4] [1 0 1]] Matrix Power is: [[10 6 14] [13 10 21] [ 2 2 4]] The array is: [[1 2] [2 1]] Matrix Power is: [[1 2] [2 1]]
Explanation
In this example, we have first imported numpy and linalg. Then we have created a matrix of size 3×3, and then we have calculated matrix_power when the value of n is 2.
After that, we have declared one more matrix of size 2×2 and called matrix_power when n=1. We got an array of the same shape after calling the function, the matrix’s power.
Program when the value of N is 0 or less than 0
See the following code.
# Program when the value of N is greater than 0
from numpy import linalg as LA
import numpy as np
arr1 = np.array([[1, 2, 3], [3, 2, 4], [1, 0, 1]])
print("The array is:\n", arr1)
# When n=0
print("Matrix Power is:\n", LA.matrix_power(arr1, 0))
arr2 = np.array([[1, 2], [2, 1]])
print("The array is:\n", arr2)
# When n=-2
print("Matrix Power is:\n", LA.matrix_power(arr2, -2))
Output
The array is: [[1 2 3] [3 2 4] [1 0 1]] Matrix Power is: [[1 0 0] [0 1 0] [0 0 1]] The array is: [[1 2] [2 1]] Matrix Power is: [[ 0.55555556 -0.44444444] [-0.44444444 0.55555556]]
Explanation
In this example, we have first imported numpy and linalg. Then we have created a matrix of size 3×3, and then we have calculated matrix_power when the value of n is 0.
In this case, we got a matrix as a result where only one diagonal has value 1, and the rest are 0.
After that, we have declared one more matrix of size 2×2 and called matrix_power when n= -2.
In this case, we got a matrix of the same shape as the given matrix has after calculating the power of n.
That is it for the numpy matrix_power() function.
