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 matrixÂ
import java.io.*;Â
class neveropen {Â
    // Dimension of the given matrix    static int max = 50;Â
    // 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);    }Â
    // 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;    }Â
    // The Driver code    public static void main(String[] args)    {Â
        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 },        };Â
        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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