Given an N * N matrix and the task is to check matrix is an idempotent matrix or not.
Idempotent matrix: A matrix is said to be an idempotent matrix if the matrix multiplied by itself returns the same matrix. The matrix M is said to be an idempotent matrix if and only if M * M = M. In an 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.
Javascript
<script> // Javascript program to check given matrix // is idempotent matrix or not.var N = 3;// Function for matrix multiplication.function multiply(mat, res){ for (var i = 0; i < N; i++) { for (var j = 0; j < N; j++) { res[i][j] = 0; for (var k = 0; k < N; k++) res[i][j] += mat[i][k] * mat[k][j]; } } return res;}// Function to check idempotent// property of matrix.function checkIdempotent(mat){ // Calculate multiplication of matrix // with itself and store it into res. var res = Array.from(Array(N), ()=>Array(N).fill(0)); res = multiply(mat, res); for (var i = 0; i < N; i++) { for (var j = 0; j < N; j++) { if (mat[i][j] != res[i][j]) return false; } } return true;}// Driver codevar mat = [[2, -2, -4], [-1, 3, 4], [1, -2, -3]]; // checkIdempotent function call.if (checkIdempotent(mat)) document.write( "Idempotent Matrix");else document.write("Not Idempotent Matrix.");// This code is contributed by noob2000.</script> |
Output:
Idempotent Matrix
Time Complexity: O(N3)
Auxiliary Space: O(N2)
Please refer complete article on Program to check idempotent matrix for more details!
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