# Program to find Normal and Trace of a matrix

Given a 2D matrix, the task is to find Trace and Normal of matrix.
Normal of a matrix is defined as square root of sum of squares of matrix elements.
Trace of a n x n square matrix is sum of diagonal elements.

Examples :

```Input : mat[][] = {{7, 8, 9},
{6, 1, 2},
{5, 4, 3}};
Output : Normal = 16
Trace  = 11
Explanation :
Normal = sqrt(7*7+ 8*8 + 9*9 + 6*6 +
1*1 + 2*2 + 5*5 + 4*4 + 3*3)
= 16
Trace  = 7+1+3 = 11

Input :mat[][] = {{1, 2, 3},
{6, 4, 5},
{2, 1, 3}};
Output : Normal = 10
Trace = 8
Explanation :
Normal = sqrt(1*1 +2*2 + 3*3 + 6*6 + 4*4 +
5*5 + 2*2 + 1*1 + 3*3)
Trace = 8(1+4+3)```

Implementation:

## C++

 `// C++ program to find trace and normal``// of given matrix``#include``using` `namespace` `std;` `// Size of given matrix``const` `int` `MAX = 100;` `// Returns Normal of a matrix of size n x n``int` `findNormal(``int` `mat[][MAX], ``int` `n)``{``    ``int` `sum = 0;``    ``for` `(``int` `i=0; i

## Java

 `// Java program to find trace and normal``// of given matrix` `import` `java.io.*;` `class` `GFG {` `// Size of given matrix``static`  `int` `MAX = ``100``;` `// Returns Normal of a matrix of size n x n`` ``static` `int` `findNormal(``int` `mat[][], ``int` `n)``{``    ``int` `sum = ``0``;``    ``for` `(``int` `i=``0``; i

## Python3

 `# Python3 program to find trace and ``# normal of given matrix ``import` `math` `# Size of given matrix ``MAX` `=` `100``; ` `# Returns Normal of a matrix ``# of size n x n ``def` `findNormal(mat, n): ` `    ``sum` `=` `0``; ``    ``for` `i ``in` `range``(n): ``        ``for` `j ``in` `range``(n): ``            ``sum` `+``=` `mat[i][j] ``*` `mat[i][j]; ``    ``return` `math.floor(math.sqrt(``sum``)); ` `# Returns trace of a matrix of ``# size n x n ``def` `findTrace(mat, n): ` `    ``sum` `=` `0``; ``    ``for` `i ``in` `range``(n): ``        ``sum` `+``=` `mat[i][i]; ``    ``return` `sum``; ` `# Driver Code ``mat ``=` `[[``1``, ``1``, ``1``, ``1``, ``1``], ``       ``[``2``, ``2``, ``2``, ``2``, ``2``], ``       ``[``3``, ``3``, ``3``, ``3``, ``3``], ``       ``[``4``, ``4``, ``4``, ``4``, ``4``], ``       ``[``5``, ``5``, ``5``, ``5``, ``5``]]; ` `print``(``"Trace of Matrix ="``, findTrace(mat, ``5``)); ` `print``(``"Normal of Matrix ="``, findNormal(mat, ``5``)); ` `# This code is contributed by mits`

## C#

 `// C# program to find trace and normal``// of given matrix``using` `System;` `class` `GFG {``    ` `    ``// Returns Normal of a matrix of``    ``// size n x n``    ``static` `int` `findNormal(``int` `[,]mat, ``int` `n)``    ``{``        ``int` `sum = 0;``        ` `        ``for` `(``int` `i = 0; i < n; i++)``            ``for` `(``int` `j = 0; j < n; j++)``                ``sum += mat[i,j] * mat[i,j];``                ` `        ``return` `(``int``)Math.Sqrt(sum);``    ``}``    ` `    ``// Returns trace of a matrix of size ``    ``// n x n``    ``static` `int` `findTrace(``int` `[,]mat, ``int` `n)``    ``{``        ``int` `sum = 0;``        ` `        ``for` `(``int` `i = 0; i < n; i++)``            ``sum += mat[i,i];``            ` `        ``return` `sum;``    ``}``    ` `    ``// Driven source``    ``public` `static` `void` `Main () ``    ``{``        ``int` `[,]mat = { {1, 1, 1, 1, 1},``                       ``{2, 2, 2, 2, 2},``                       ``{3, 3, 3, 3, 3},``                       ``{4, 4, 4, 4, 4},``                       ``{5, 5, 5, 5, 5},``    ``};` `    ``Console.Write (``"Trace of Matrix = "``            ``+ findTrace(mat, 5) + ``"\n"``);``    ``Console.Write(``"Normal of Matrix = "``                    ``+ findNormal(mat, 5));``        ` `    ``}``} ` `// This code is contributed by nitin mittal.`

## PHP

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## Javascript

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Output
```Trace of Matrix = 15
Normal of Matrix = 16```

Time Complexity : O(n*n)
Space Complexity : O(1), since no extra space has been taken.

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