# 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)
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution. ## 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

 ` `

Output :

```Trace of matrix = 15
Normal of matrix = 16
```

Time Complexity :
O(n*n)
Space Complexity : O(1)

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