Normal and Trace of a Matrix in Java

by Online Tutorials Library July 22, 2022

Normal and Trace of a Matrix in Java

In this section, we will learn how to calculate the normal and trace of a matrix in Java. Before moving to, the program, first we will understand the what is normal and trace of a matrix.

Normal of a Matrix

The normal of a matrix is the square root of the sum of squares of all the elements of a matrix. For example, consider the following matrix.

Normal and Trace of a Matrix in Java

First, we will calculate the sum of the square of each element.

9²+ 8² + 2² + 1² + 4² + 7² + 3² + 5² + 6²

81 + 64 + 4 + 1 + 16 + 49 + 9 + 25 + 36 = 285

Now, calculate the square root of the sum of squares.

√285 = 16.8819430161

Trace of a Matrix

The trace of a matrix is the sum of all the elements present in the principal diagonal (upper left to lower right). Note that the matrix must be a square matrix (the number of rows and columns must be the same). It is useful to prove results in linear algebra. For example, consider the following matrix.

Normal and Trace of a Matrix in Java

Trace for the above matrix is 5 + 4 + 7 = 16.

Java Program to Find Normal and Trace of a Matrix

MatrixNormalTrace1.java

  import java.util.*;  public class MatrixNormalTrace1  {      public static void main(String args[])      {          int array[][] = new int[5][5];          int i, j;          double sum = 0, square = 0, result = 0;    Scanner s = new Scanner(System.in);    System.out.print(“Enter the number of rows: “);    //reads number of rows from the user    int row = s.nextInt();    System.out.print(“Enter the number of columns: “);    //reads number of columns from the user    int column = s.nextInt();  System.out.println(“Enter matrix:”);  //loop for rows   for(i = 0; i < row; i++)    {        //loop for columns         for(j = 0; j < column; j++)            {               //reads the matrix elements                 array[i][j] = s.nextInt();                //prints space                  System.out.print(” “);           }          }  System.out.println(“You have entered the following matrix: “);  //prints the matrix   for(i = 0; i < row; i++)          {            for(j = 0; j < column; j++)              {           System.out.print(array[i][j]+” “);              }              System.out.println(” “);      }          System.out.println(“The trace of the given matrix is: “);    for(i = 0; i < row; i++)    {            for(j = 0; j < column; j++)             {                 //checks if an element is of the same rows and column or not, if same calculates trace of the matrix                  if(i == j)               {                   //find the sum of principal diagonal                      sum = sum + (array[i][j]);                  }              }          }          //prints trace          System.out.println(sum);            System.out.println(“The normal of the given matrix is: “);                for(i = 0; i < row; i++)     {          for(j = 0; j < column; j++)             {                 //calculates the sum of square of matrix elements                  square = square + (array[i][j])*(array[i][j]);              }      }      //calculates square root of the sum          result = Math.sqrt(square);          //prints normal of the given matrix          System.out.println(result);      }  }  

Output:

Normal and Trace of a Matrix in Java

Similarly, we can also find the normal and trace of a matrix using function.

MatrixNormalTrace2.java

  import java.io.*;  public class MatrixNormalTrace2  {  //size of the given matrix  static int MAX = 10;  //the method calculates and returns Normal of a matrix   static int calculateNormal(int matrix[][], int n)  {  int sum = 0;  for (int i=0; i;>

Output:

Normal and Trace of a Matrix in Java

Next TopicRight View of a Binary Tree in Java

Normal and Trace of a Matrix in Java

Normal and Trace of a Matrix in Java

Normal of a Matrix

Trace of a Matrix

Java Program to Find Normal and Trace of a Matrix

Lombok Java

Polygonal Number in Java

You may also like