How to find the trace of a matrix

What is the trace of a matrix?

The sum of the principal diagonal elements is called the trace of the matrix.

For example, consider the following 2x2 matrix.

[1, 2, 3]
[4, 5, 6]
[7, 8, 9]

The trace of the matrix above is as follows:

1 + 5 + 9 = 15

Trace - 1 + 5 + 9 = 15

Algorithm

  1. Initialise a variable, i.e., trace, to zero.
  2. Iterate through the elements of the principal diagonal elements with the help of a for loop.
    1. Add the diagonal element to the trace variable.

Note: Diagonal elements have row numbers equal to the column numbers.

  1. Return the trace value.
  • Time complexity - O(N)
  • Space complexity - O(1)

Example

import java.util.Arrays;
public class Main{
    private static int computeTrace(int[][] matrix){
        int trace = 0;
        // Run a loop iterating the diagonal elements
        for (int i = 0; i < matrix.length; i++){
            // diagonal elements have row number = column number
            trace += matrix[i][i];
        }
        return trace;
    }
    private static void printMatrix(int[][] matrix){
        for (int[] row : matrix)
            System.out.println(Arrays.toString(row));
    }
    public static void main(String[] args){
        int matrix[][] = {{1, 2, 3},
                {4, 5, 6},
                {7, 8 , 9}
        };
        int trace = computeTrace(matrix);
        printMatrix(matrix);
        System.out.println("Trace of the above matrix is " + trace);
    }
}
Trace of Matrix

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