# Java Program to Find the Normal and Trace of a Matrix

For a given 2D matrix, the purpose is to find the Trace and Normal of the matrix.

Normal of a matrix is defined as the square root of the sum of squares of all the elements of the matrix.

Trace of a given square matrix is defined as the sum of all the elements in the diagonal.

Examples :

```Input : matrix[][] = {{1, 4, 4},
{2, 3, 7},
{0, 5, 1}};
Output : Normal = 11
Trace  = 5
Explanation :
Normal = sqrt(1*1+ 4*4 + 4*4 + 2*2 +
3*3 + 7*7 + 0*0 + 5*5 + 1*1)
= 11
Trace  = 1+3+1 = 5

Input :matrix[][] = {{8, 9, 11},
{0, 1, 15},
{4, 10, -7}};
Output : Normal = 25
Trace  = 2
Explanation :
Normal = sqrt(8*8 +9*9 + 11*11 + 0*0 + 1*1 +
15*15 + 4*4 + 10*10 + -7*-7) = 25
Trace  = (8+1-7) = 2``` Example:

## Java

 `// Java program to find the trace` `// and normal of the given matrix`   `import` `java.io.*;`   `class` `geeksforgeeks {`   `    ``// Dimension of the given matrix` `    ``static` `int` `max = ``50``;`   `    ``// Finds Normal of the given` `    ``// matrix of size N x N` `    ``static` `int` `Normal(``int` `matrix[][], ``int` `N)` `    ``{` `        ``// Initializing sum` `        ``int` `s = ``0``;` `        ``for` `(``int` `j = ``0``; j < N; j++)` `            ``for` `(``int` `k = ``0``; k < N; k++)` `                ``s += matrix[j][k] * matrix[j][k];` `        ``return` `(``int``)Math.sqrt(s);` `    ``}`   `    ``// Finds trace of the given` `    ``// matrix of size N x N` `    ``static` `int` `Trace(``int` `matrix[][], ``int` `N)` `    ``{` `        ``int` `s = ``0``;` `        ``for` `(``int` `j = ``0``; j < N; j++)` `            ``s += matrix[j][j];` `        ``return` `s;` `    ``}`   `    ``// The Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{`   `        ``int` `matrix[][] = {` `            ``{ ``2``, ``3``, ``5``, ``6``, ``7` `},      { ``8``, ``9``, ``10``, ``11``, ``12` `},` `            ``{ ``13``, ``14``, ``15``, ``16``, ``17` `}, { ``18``, ``1``, ``3``, ``0``, ``6` `},` `            ``{ ``7``, ``8``, ``11``, ``8``, ``11` `},` `        ``};`   `        ``System.out.println(``"Trace of the Matrix is: "` `                           ``+ Trace(matrix, ``5``));` `        ``System.out.println(``"Normal of the Matrix is: "` `                           ``+ Normal(matrix, ``5``));` `    ``}` `}`

Output

```Trace of the Matrix is: 37
Normal of the Matrix is: 50```

Time Complexity: O(N*N), as we are using nested loops for traversing the matrix.

Auxiliary Space: O(1), as we are not using any extra space.

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