Java Program to Check If a Matrix Is a Lower Triangular Matrix

Java program to check if a given matrix is a lower triangular has been shown here. A square matrix is considered a lower triangular matrix if all the elements above the main diagonal are Zero. The elements in the main diagonal may or may not be 0.

Examples:

In the given examples, (i), (ii), (iv) and (v) are lower triangular matrices as every element above the principal diagonal is 0 in each of these matrices. The matrix shown in (iii) is not a lower triangular matrix as one element above the principal diagonal is non-zero. The dotted lines have been drawn over the principal diagonals.

Page content(s):

1. Algorithm

2. Pseudocode

3. Time Complexity

4. Program & Output

1. Algorithm to Check If a Matrix Is a Lower Triangular Matrix

1. Take a matrix $A_{m\times n}$ as input

2. Check if $m=n$

3. If step [2] is false then display "Input matrix is not a square matrix!" and exit program

4. If step [2] is true, then

5. Check if $A_{i,j} \neq 0$ for each $i < j$ and $i \in [1, m]$ and $j \in [1, n]$

6. If step [5] is true for atleast one $A_{i,j}$ then display "The matrix is not a lower triangular matrix" and exit program.

7. If step [5] is false then display "The matrix is a lower triangular matrix" and exit program.

2. Pseudocode to Check If a Matrix Is a Lower Triangular Matrix

Input: A matrix $A_{m\times n}$

Output: A is lower triangular or not

1. Procedure lowerTriangularMatrix($A_{m\times n}$):

2. If $m == n$:

3. Repeat for each $i < j$ where $i \in [1, m]$ and $j \in [1, n]$

4. If $A_{i,j} \neq 0$:

5. Return Not a lower triangular matrix

6. Return A lower triangular matrix

7. Else:

8. Return It should be a square matrix

9. End Procedure

3. Time Complexity to Check If a Matrix Is a Lower Triangular Matrix

Time Complexity: O($mn$)

Where $m$ is the number of rows and $n$ is the number of columns in the matrices.

4. Java Program to Check If a Matrix Is a Lower Triangular Matrix

Code has been copied

/**********************************
        alphabetacoder.com
 Java Program to check if a matrix 
   is a lower triangular matrix
***********************************/

import java.util.Scanner;

class Main {
    public static void main(String args[]) {
        // declare object of Scanner class
        Scanner sc = new Scanner(System.in);

        // declare variables
        int m, n, i, j, flag = 0;
        int[][] A = new int[10][10];

        //take input of the order of the matrix
        System.out.print("Enter the number of rows and columns of matrix = ");
        m = sc.nextInt();
        n = sc.nextInt();

        //take input of the first matrix
        System.out.println("Enter the elements of matrix of order " + m + " x " + n + " = ");
        for (i = 0; i < m; i++)
            for (j = 0; j < n; j++)
                A[i][j] = sc.nextInt();

        // check if the matrix is a square matrix or not
        // if it is square matrix, check if it is lower triangular or not
        if (m != n)
            System.out.println("\nInput matrix is not a square matrix!\n");
        else {
            // check if A is lower triangular or not by
            // finding an non-zero element above main diagonal 
            for (i = 0; i < m; i++) {
                for (j = i + 1; j < n; j++) {
                    if (A[i][j] != 0) {
                        // non-zero element found
                        flag = 1;
                        break;
                    }
                }
                // break the loop as non-zero element 
                // above main diagonal has been detected
                if (flag == 1)
                    break;
            }

            // display the result
            if (flag == 0)
                System.out.print("\nIt is a lower triangular matrix!");
            else
                System.out.print("\nIt is not a lower triangular matrix!");
        }
    }
}

Output

Enter the number of rows and columns of matrix = 4 4

Enter the elements of matrix of order 4 x 4 =

5 0 0 0

3 0 0 0

4 3 7 0

2 1 3 4

It is a lower triangular matrix!