# 程序檢查矩陣是否為下三角 > 原文： [https://www.geeksforgeeks.org/program-check-matrix-lower-triangular/](https://www.geeksforgeeks.org/program-check-matrix-lower-triangular/) 給定一個正方形矩陣，任務是檢查矩陣是否為下三角形式。 如果主對角線上的所有條目均為零，則將方陣稱為下三角。  示例： ``` 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. ``` ## C++ ```cpp // Program to check lower // triangular matrix. #include <bits/stdc++.h> #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; 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 // 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; 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 ```py # 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# ```cs // 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 ```php <?php // PHP Program to check lower // triangular matrix. $N = 4; // Function to check matrix is in? // lower triangular form or not. function isLowerTriangularMatrix($mat) { ????global $N; ????for ($i = 0; $i < $N; $i++) ????????for ($j = $i + 1; $j < $N; $j++) ????????????if ($mat[$i][$j] != 0) ????????????????return false; ????return true; } // Driver Code $mat = array(array( 1, 0, 0, 0 ), ?????????????array( 1, 4, 0, 0 ), ?????????????array( 4, 6, 2, 0 ), ?????????????array( 0, 4, 7, 6 ));? // Function call if (isLowerTriangularMatrix($mat)) ????echo("Yes"); else ????echo("No"); // This code is contributed by Ajit. ?> ``` Output: ``` Yes ``` * * * * * *