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 Matrix
Input : mat[N][N] = {{2, -2, -4},
{-1, 3, 4},
{1, -2, -3}}
Output : Idempotent Matrix.
Java
// Java program to check given matrix// is idempotent matrix or not.import java.io.*;class GFG{ static int N = 3; // Function for matrix multiplication. static void multiply(int mat[][], int res[][]) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { res[i][j] = 0; for (int k = 0; k < N; k++) res[i][j] += mat[i][k] * mat[k][j]; } } } // Function to check idempotent // property of matrix. static boolean checkIdempotent(int mat[][]) { // Calculate multiplication of matrix // with itself and store it into res. int res[][] = new int[N][N]; multiply(mat, res); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { if (mat[i][j] != res[i][j]) return false; } } return true; } // Driver code. public static void main (String[] args) { int mat[][] = {{2, -2, -4}, {-1, 3, 4}, {1, -2, -3}}; // checkIdempotent function call. if (checkIdempotent(mat)) System.out.println( "Idempotent Matrix"); else System.out.println("Not Idempotent Matrix."); }}// This code is contributed by vt_m. |
Output:
Idempotent Matrix
Time complexity: O(N3)
Auxiliary space: O(N2)
Please refer complete article on Program to check idempotent matrix for more details!
