Given a N * N matrix and the task is to check matrix is idempotent matrix or not.
Idempotent matrix: A matrix is said to be idempotent matrix if matrix multiplied by itself return the same matrix. The matrix M is said to be idempotent matrix if and only if M * M = M. In idempotent matrix M is a square matrix.
Examples:
Input : mat[][] = {{3, -6}, {1, -2}};
Output: Idempotent MatrixInput : mat[N][N] = {{2, -2, -4}, {-1, 3, 4}, {1, -2, -3}}
Output : Idempotent Matrix.
Python 3
# Python Program to check given matrix # is idempotent matrix or not.import math# Function for matrix multiplication.def multiply(mat, res): N= len(mat) for i in range(0,N): for j in range(0,N): res[i][j] = 0 for k in range(0,N): res[i][j] += mat[i][k] * mat[k][j]# Function to check idempotent# property of matrix.def checkIdempotent(mat): N= len(mat) # Calculate multiplication of matrix # with itself and store it into res. res =[[0]*N for i in range(0,N)] multiply(mat, res) for i in range(0,N): for j in range(0,N): if (mat[i][j] != res[i][j]): return False return True# driver Functionmat = [ [2, -2, -4], [-1, 3, 4], [1, -2, -3] ] # checkIdempotent function call.if (checkIdempotent(mat)): print("Idempotent Matrix")else: print("Not Idempotent Matrix.")# This code is contributed by Gitanjali. |
Idempotent Matrix
Time Complexity: O(N3)
Auxiliary Space: O(N2)
Please refer complete article on Program to check idempotent matrix for more details!
Using Numpy:
Install Numpy using command
pip install numpy
This method converts the matrix to a numpy array and uses the @ operator to perform matrix multiplication. The all() function is used to check if all elements in the comparison are True.
Python3
import numpy as npdef is_idempotent(matrix): # Convert the matrix to a numpy array arr = np.array(matrix) # Check if the matrix multiplied by itself is equal to the original matrix return (arr @ arr == arr).all()matrix = [[3, -6], [1, -2]]print(is_idempotent(matrix)) # Truematrix = [[2, -2, -4], [-1, 3, 4], [1, -2, -3]]print(is_idempotent(matrix)) # Truematrix = [[1, 2], [3, 4]]print(is_idempotent(matrix)) # False#This code is contributed by Edula Vinay Kumar Reddy |
Output:
True True False
Time complexity: O(n^2)
Auxiliary Space: O(n^2)
