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 matriximport java.io.*;class neveropen { // 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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