In the lower triangular matrix, the elements that are present above the diagonal should be 0. Given a matrix and the task is to check the matrix is in lower triangular form or not. A matrix must be a square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero.
Example –
Input:
1 0 0
1 2 0
1 2 3
Output: Matrix is lower triangular matrix
Input:
1 2 2
2 1 1
2 2 2
Output: Matrix is not a lower triangular matrix
Approach:
- Check if the given matrix is square or not.
- If yes, then traverse the upper triangle part matrix.
- Check if all the entries above the main diagonal are zero.
- If yes, then print Matrix is a lower triangular matrix.
Below is the implementation of the above approach:
Java
// Java Program to check for// a lower triangular matrix.import java.util.Scanner;public class LowerTriangularMatrix { public static boolean isLowerTriangularMatrix(int[][] matrix) { for (int i = 0; i < matrix[0].length; i++) { for (int j = i + 1; j < matrix[0].length; j++) { if (matrix[i][j] != 0) return false; } } return true; } public static void main(String args[]) { int rows = 3, columns = 3; // returns true if number of rows and columns are // equal else false if (rows == columns) { // initializing the matrix int Matrix[][] = { { 1, 0, 0 }, { 2, 3, 0 }, { 5, 6, 7 } }; // Display the values of matrix System.out.println("Matrix is : "); for (int i = 0; i < rows; i++) { for (int j = 0; j < columns; j++) { System.out.print(Matrix[i][j] + "\t"); } System.out.println(); } // Function call boolean result = isLowerTriangularMatrix(Matrix); // returns true if matrix is lower triangular // matrix else false if (result == true) { System.out.println( "Matrix is lower triangular matrix"); } else { System.out.println( "Matrix is not lower triangular matrix"); } } else { System.out.println( "Number of rows and number of columns should be equal"); } }} |
Output
Matrix is : 1 0 0 2 3 0 5 6 7 Matrix is lower triangular matrix
Time Complexity: O(N2), where N is the length of the row in a square matrix.
Auxiliary Space: O(1), no extra space is required, so it is a constant.