C 程序檢查矩陣是否傾斜對稱 · GeeksForGeeks 中文系列教程

# C 程序檢查矩陣是否傾斜對稱 > 原文： [https://www.geeksforgeeks.org/c-program-check-whether-matrix-skew-symmetric-not/](https://www.geeksforgeeks.org/c-program-check-whether-matrix-skew-symmetric-not/) 傾斜對稱矩陣或反對稱矩陣是方陣，其轉置與原始矩陣的轉置相反。如果矩陣的第 i <sup>行</sup>行和第 j <sup>行</sup>列中的條目為 a [i] [j]，即如果 A =（a [i] [j]），傾斜對稱條件為-A = -a [j] [i]。 **示例**： ``` Input : matrix: 0 5 -4 -5 0 1 4 -1 0 Output: Transpose matrix: 0 -5 4 5 0 1 -4 1 0 Skew Symmetric matrix ``` **步驟**： 1. 找到輸入矩陣的轉置。 2. 如果輸入矩陣等于其轉置矩陣的負值，則該矩陣為“斜對稱”。 ## C++ ```cpp // C program to check whether given matrix // is skew-symmetric or not #include <stdio.h> #include <stdlib.h> #define ROW 3 #define COL 3 // Utility function to create transpose matrix void transpose(int transpose_matrix[ROW][COL], ?????????????????????????int matrix[ROW][COL]) { ???for (int i = 0; i < ROW; i++) ??????for (int j = 0; j < COL; j++) ?????????transpose_matrix[j][i] = matrix[i][j]; } // Utility function to check skew - symmetric // matrix condition bool check(int transpose_matrix[ROW][COL], ????????????????????int matrix[ROW][COL]) { ????for (int i = 0; i < ROW; i++) ????????for (int j = 0; j < COL; j++) ????????????if (matrix[i][j] != -transpose_matrix[i][j]) ????????????????return false; ????return true; } // Utility function to print a matrix void printMatrix(int matrix[ROW][COL]) { ????for (int i = 0; i < ROW; i++) ????{ ???????for (int j = 0; j < COL; j++) ????????????printf("%d ", matrix[i][j]); ???????printf("\n"); ????} } // Driver program to test above functions int main() { ????int matrix[ROW][COL] = { ????????????????????????????{0, 5, -4}, ????????????????????????????{-5, 0, 1}, ????????????????????????????{4, -1, 0}, ???????????????????????????}; ????int transpose_matrix[ROW][COL]; ????// Function create transpose matrix ????transpose(transpose_matrix, matrix); ????printf ("Transpose matrix: \n"); ????printMatrix(transpose_matrix); ????// Check whether matrix is skew-symmetric or not ????if (check(transpose_matrix, matrix)) ???????printf("Skew Symmetric Matrix"); ????else ???????printf("Not Skew Symmetric Matrix"); ????return 0; } ``` ## Java ```java // java program to check // whether given matrix // is skew-symmetric or not import java.io.*; class GFG { static int ROW =3; static int COL =3; // Utility function to create transpose matrix ?static void transpose(int transpose_matrix[][], ????????????????????????int matrix[][]) { for (int i = 0; i < ROW; i++) ????for (int j = 0; j < COL; j++) ????????transpose_matrix[j][i] = matrix[i][j]; } // Utility function to check skew - symmetric // matrix condition ?static boolean check(int transpose_matrix[][], ????????????????????int matrix[][]) { ????for (int i = 0; i < ROW; i++) ????????for (int j = 0; j < COL; j++) ????????????if (matrix[i][j] != -transpose_matrix[i][j]) ????????????????return false; ????return true; } // Utility function to print a matrix ?static void printMatrix(int matrix[][]) { ????for (int i = 0; i < ROW; i++) ????{ ????for (int j = 0; j < COL; j++) ????????????System.out.print(matrix[i][j] + " "); ????System.out.println(); ????} } // Driver program to test above functions public static void main (String[] args) { ????????int matrix[][] = { ????????????????????????????{0, 5, -4}, ????????????????????????????{-5, 0, 1}, ????????????????????????????{4, -1, 0}, ????????????????????????}; ????int transpose_matrix[][] = new int[ROW][COL]; ????// Function create transpose matrix ????transpose(transpose_matrix, matrix); ????System.out.println ("Transpose matrix: "); ????printMatrix(transpose_matrix); ????// Check whether matrix is skew-symmetric or not ????if (check(transpose_matrix, matrix)) ????System.out.println("Skew Symmetric Matrix"); ????else ????System.out.println("Not Skew Symmetric Matrix"); ????} } // This code is contributed by vt_m. ``` ## Python3 ```py # Python 3 program to check # whether given matrix # is skew-symmetric or not ROW=3 COL=3 # Utility function to # create transpose matrix def transpose(transpose_matrix,matrix): ????for i in range (ROW): ????????for j in range(COL): ????????????transpose_matrix[j][i] = matrix[i][j] # Utility function to # check skew - symmetric # matrix condition def check(transpose_matrix,matrix): ????for i in range(ROW): ????????for j in range(COL): ????????????if (matrix[i][j] != -transpose_matrix[i][j]): ????????????????return False ????return True # Utility function to print a matrix def printMatrix(matrix): ????for i in range (ROW): ????????for j in range(COL): ????????????print(matrix[i][j]," ",end="") ????????print() # Driver program to test above functions matrix= [ ????????????[0, 5, -4], ????????????[-5, 0, 1], ????????????[4, -1, 0], ????????] transpose_matrix=[[0 for i in range(3)] for j in range(3)] # Function create transpose matrix transpose(transpose_matrix, matrix) print("Transpose matrix:") printMatrix(transpose_matrix) # Check whether matrix is # skew-symmetric or not if (check(transpose_matrix, matrix)): ????print("Skew Symmetric Matrix") else: ????print("Not Skew Symmetric Matrix") # This code is contributed # by Azkia Anam. ``` ## C# ```cs // C# program to check // whether given matrix // is skew-symmetric or not using System; class GFG? { static int ROW =3; static int COL =3; // Utility function to // create transpose matrix static void transpose(int [,]transpose_matrix, ??????????????????????int [,]matrix) { for (int i = 0; i < ROW; i++) ????for (int j = 0; j < COL; j++) ????????transpose_matrix[j,i] = matrix[i,j]; } // Utility function to check? // skew - symmetric matrix? // condition static bool check(int [,]transpose_matrix, ??????????????????int [,]matrix) { ????for (int i = 0; i < ROW; i++) ????????for (int j = 0; j < COL; j++) ????????????if (matrix[i, j] !=? ????????????????-transpose_matrix[i, j]) ????????????????return false; ????return true; } // Utility function // to print a matrix static void printMatrix(int [,]matrix) { ????for (int i = 0; i < ROW; i++) ????{ ????for (int j = 0; j < COL; j++) ????????????Console.Write(matrix[i, j] +? ???????????????????????????????????" "); ????Console.WriteLine(); ????} } // Driver Code public static void Main ()? { ????int [,]matrix = {{0, 5, -4}, ?????????????????????{-5, 0, 1}, ?????????????????????{4, -1, 0},}; ????int [,]transpose_matrix = new int[ROW, COL]; ????// Function create transpose matrix ????transpose(transpose_matrix, matrix); ????Console.WriteLine("Transpose matrix: "); ????printMatrix(transpose_matrix); ????// Check whether matrix is ????// skew-symmetric or not ????if (check(transpose_matrix, matrix)) ????Console.WriteLine("Skew Symmetric Matrix"); ????else ????Console.WriteLine("Not Skew Symmetric Matrix"); ????} } // This code is contributed by anuj_67\. ``` **輸出**： ``` Transpose matrix: 0 -5 4 5 0 -1 -4 1 0 Skew Symmetric Matrix ``` **參考**： [維基百科](https://en.wikipedia.org/wiki/Skew-symmetric_matrix)