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:Â
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>Â Â // Javascript program to check given matrix // is idempotent matrix or not.var N = 3;Â
// Function for matrix multiplication.function multiply(mat, res){Â Â Â Â for (var i = 0; i < N; i++)Â Â Â Â {Â Â Â Â Â Â Â Â for (var j = 0; j < N; j++)Â Â Â Â Â Â Â Â {Â Â Â Â Â Â Â Â Â Â Â Â res[i][j] = 0;Â Â Â Â Â Â Â Â Â Â Â Â for (var k = 0; k < N; k++)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â res[i][j] += mat[i][k] * mat[k][j];Â Â Â Â Â Â Â Â }Â Â Â Â }Â Â Â Â return res;}Â
// Function to check idempotent// property of matrix.function checkIdempotent(mat){ Â
    // 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);Â
    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;}Â
// 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.");Â
// 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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