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= 11Trace= 5Explanation :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 = 5Input:matrix[][] = {{8, 9, 11}, {0, 1, 15}, {4, 10, -7}};Output:Normal= 25Trace= 2Explanation :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

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