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# Program to check if matrix is lower triangular

• Difficulty Level : Basic
• Last Updated : 27 Jul, 2022

Given a square matrix and the task is to check the matrix is in lower triangular form or not. A square matrix is called lower triangular if all the entries above the main diagonal are zero.

Examples:

```Input : mat[4][4] = {{1, 0, 0, 0},
{1, 4, 0, 0},
{4, 6, 2, 0},
{0, 4, 7, 6}};
Output : Matrix is in lower triangular form.

Input : mat[4][4] = {{1, 0, 0, 0},
{4, 3, 0, 1},
{7, 9, 2, 0},
{8, 5, 3, 6}};
Output : Matrix is not in lower triangular form.```

Implementation:

## C++

 `// Program to check lower``// triangular matrix.``#include ``#define N 4``using` `namespace` `std;` `// Function to check matrix is in``// lower triangular form or not.``bool` `isLowerTriangularMatrix(``int` `mat[N][N])``{``    ``for` `(``int` `i = 0; i < N-1; i++)``        ``for` `(``int` `j = i + 1; j < N; j++)``            ``if` `(mat[i][j] != 0)``                ``return` `false``;``    ``return` `true``;``}` `// Driver function.``int` `main()``{``    ``int` `mat[N][N] = { { 1, 0, 0, 0 },``                      ``{ 1, 4, 0, 0 },``                      ``{ 4, 6, 2, 0 },``                      ``{ 0, 4, 7, 6 } };` `    ``// Function call``    ``if` `(isLowerTriangularMatrix(mat))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;``    ``return` `0;``}`

## Java

 `// Java Program to check for``// a lower triangular matrix.``import` `java.io.*;` `class` `Lower_triangular``{``    ``int` `N = ``4``;` `    ``// Function to check matrix is``    ``// in lower triangular form or not.``    ``boolean` `isLowerTriangularMatrix(``int` `mat[][])``    ``{``        ``for` `(``int` `i = ``0``; i < N-``1``; i++)``            ``for` `(``int` `j = i + ``1``; j < N; j++)``                ``if` `(mat[i][j] != ``0``)``                    ``return` `false``;` `        ``return` `true``;``    ``}` `    ``// Driver function.``    ``public` `static` `void` `main(String args[])``    ``{``        ``Lower_triangular ob = ``new` `Lower_triangular();``        ``int` `mat[][] = { { ``1``, ``0``, ``0``, ``0` `},``                        ``{ ``1``, ``4``, ``0``, ``0` `},``                        ``{ ``4``, ``6``, ``2``, ``0` `},``                        ``{ ``0``, ``4``, ``7``, ``6` `} };``                        ` `        ``// Function call``        ``if` `(ob.isLowerTriangularMatrix(mat))``            ``System.out.println(``"Yes"``);``        ``else``            ``System.out.println(``"No"``);``    ``}``}` `// This code is contributed by Anshika Goyal.`

## Python3

 `# Python3 Program to check``# lower triangular matrix.` `# Function to check matrix``# is in lower triangular``def` `islowertriangular(M):``    ``for` `i ``in` `range``(``0``, ``len``(M)):``        ``for` `j ``in` `range``(i ``+` `1``, ``len``(M)):``            ``if``(M[i][j] !``=` `0``):``                    ``return` `False``    ``return` `True``    ` `# Driver function.``M ``=` `[[``1``,``0``,``0``,``0``],``     ``[``1``,``4``,``0``,``0``],``     ``[``4``,``6``,``2``,``0``],``     ``[``0``,``4``,``7``,``6``]]` `if` `islowertriangular(M):``    ``print` `(``"Yes"``)``else``:``    ``print` `(``"No"``)``    ` `# This code is contributed by Anurag Rawat`

## C#

 `// C# program to check for``// a lower triangular matrix.``using` `System;` `class` `Lower_triangular``{``    ``int` `N = 4;` `    ``// Function to check matrix is``    ``// in lower triangular form or not.``    ``bool` `isLowerTriangularMatrix(``int``[, ] mat)``    ``{``        ``for` `(``int` `i = 0; i < N; i++)``            ``for` `(``int` `j = i + 1; j < N; j++)``                ``if` `(mat[i, j] != 0)``                    ``return` `false``;` `        ``return` `true``;``    ``}` `    ``// Driver function.``    ``public` `static` `void` `Main()``    ``{``        ``Lower_triangular ob = ``new` `Lower_triangular();``        ``int``[, ] mat = { { 1, 0, 0, 0 },``                        ``{ 1, 4, 0, 0 },``                        ``{ 4, 6, 2, 0 },``                        ``{ 0, 4, 7, 6 } };` `        ``// Function call``        ``if` `(ob.isLowerTriangularMatrix(mat))``            ``Console.WriteLine(``"Yes"``);``        ``else``            ``Console.WriteLine(``"No"``);``    ``}``}` `// This code is contributed by vt_m.`

## PHP

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## Javascript

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Output

`Yes`

Time Complexity: O(n2), where n represents the number of rows and columns of the matrix.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

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