# Finding the Frobenius Norm of a given matrix

Given an M * N matrix, the task is to find the Frobenius Norm of the matrix. The Frobenius Norm of a matrix is defined as the square root of the sum of the squares of the elements of the matrix.

Example:

Input: mat[][] = {{1, 2}, {3, 4}}
Output: 5.47723
sqrt(12 + 22 + 32 + 42) = sqrt(30) = 5.47723

Input: mat[][] = {{1, 4, 6}, {7, 9, 10}}
Output: 16.8226

Approach: Find the sum of squares of the elements of the matrix and then print the square root of the calculated value.

Below is the implementation of the above approach:

## CPP

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `const` `int` `row = 2, col = 2; ` ` `  `// Function to return the Frobenius ` `// Norm of the given matrix ` `float` `frobeniusNorm(``int` `mat[row][col]) ` `{ ` ` `  `    ``// To store the sum of squares of the ` `    ``// elements of the given matrix ` `    ``int` `sumSq = 0; ` `    ``for` `(``int` `i = 0; i < row; i++) { ` `        ``for` `(``int` `j = 0; j < col; j++) { ` `            ``sumSq += ``pow``(mat[i][j], 2); ` `        ``} ` `    ``} ` ` `  `    ``// Return the square root of ` `    ``// the sum of squares ` `    ``float` `res = ``sqrt``(sumSq); ` `    ``return` `res; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `mat[row][col] = { { 1, 2 }, { 3, 4 } }; ` ` `  `    ``cout << frobeniusNorm(mat); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach  ` `class` `GFG ` `{ ` `     `  `    ``final` `static` `int` `row = ``2``, col = ``2``;  ` `     `  `    ``// Function to return the Frobenius  ` `    ``// Norm of the given matrix  ` `    ``static` `float` `frobeniusNorm(``int` `mat[][])  ` `    ``{  ` `     `  `        ``// To store the sum of squares of the  ` `        ``// elements of the given matrix  ` `        ``int` `sumSq = ``0``;  ` `        ``for` `(``int` `i = ``0``; i < row; i++)  ` `        ``{  ` `            ``for` `(``int` `j = ``0``; j < col; j++)  ` `            ``{  ` `                ``sumSq += (``int``)Math.pow(mat[i][j], ``2``);  ` `            ``}  ` `        ``}  ` `     `  `        ``// Return the square root of  ` `        ``// the sum of squares  ` `        ``float` `res = (``float``)Math.sqrt(sumSq);  ` `        ``return` `res;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main (String[] args) ` `    ``{  ` `        ``int` `mat[][] = { { ``1``, ``2` `}, { ``3``, ``4` `} };  ` `     `  `        ``System.out.println(frobeniusNorm(mat));  ` `     `  `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

## Python3

 `# Python3 implementation of the approach ` `from` `math ``import` `sqrt ` `row ``=` `2` `col ``=` `2` ` `  `# Function to return the Frobenius ` `# Norm of the given matrix ` `def` `frobeniusNorm(mat): ` ` `  `    ``# To store the sum of squares of the ` `    ``# elements of the given matrix ` `    ``sumSq ``=` `0` `    ``for` `i ``in` `range``(row): ` `        ``for` `j ``in` `range``(col): ` `            ``sumSq ``+``=` `pow``(mat[i][j], ``2``) ` ` `  `    ``# Return the square root of ` `    ``# the sum of squares ` `    ``res ``=` `sqrt(sumSq) ` `    ``return` `round``(res, ``5``) ` ` `  `# Driver code ` ` `  `mat ``=` `[ [ ``1``, ``2` `], [ ``3``, ``4` `] ] ` ` `  `print``(frobeniusNorm(mat)) ` ` `  `# This code is contributed by mohit kumar 29 `

## C#

 `// C# implementation of the approach  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``static` `int` `row = 2, col = 2;  ` `     `  `    ``// Function to return the Frobenius  ` `    ``// Norm of the given matrix  ` `    ``static` `float` `frobeniusNorm(``int` `[,]mat)  ` `    ``{  ` `     `  `        ``// To store the sum of squares of the  ` `        ``// elements of the given matrix  ` `        ``int` `sumSq = 0;  ` `        ``for` `(``int` `i = 0; i < row; i++)  ` `        ``{  ` `            ``for` `(``int` `j = 0; j < col; j++)  ` `            ``{  ` `                ``sumSq += (``int``)Math.Pow(mat[i, j], 2);  ` `            ``}  ` `        ``}  ` `     `  `        ``// Return the square root of  ` `        ``// the sum of squares  ` `        ``float` `res = (``float``)Math.Sqrt(sumSq);  ` `        ``return` `res;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main () ` `    ``{  ` `        ``int` `[,]mat = { { 1, 2 }, { 3, 4 } };  ` `     `  `        ``Console.WriteLine(frobeniusNorm(mat));  ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

Output:

```5.47723
```

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Improved By : mohit kumar 29, AnkitRai01