查找给定矩阵的转置的程序

17 Mar 2025 | 4 分钟阅读

说明

在此程序中，我们需要找到给定矩阵的转置并打印结果矩阵。

矩阵的转置

矩阵的转置可以通过交换行和列来找到，也就是说，原始矩阵的行将成为新矩阵的列。同样，原始矩阵中的列将成为新矩阵中的行。该操作可以表示如下：

[ AT ]_ij = [ A ]_ji

Program to find the transpose of a given matrix

如果原始矩阵的尺寸是 2 x 3，那么新的转置矩阵的尺寸将是 3 x 2。

算法

声明并初始化一个二维数组 a。
计算矩阵中的行数和列数，并将它们分别存储在变量 rows 和 cols 中。
声明另一个维度反转的数组 t，即 t[cols][rows]。数组 t 将用于存储转置矩阵的元素。
通过以下方式遍历数组 a 并将其行转换为矩阵 t 的列：
t[ i ][ j ] = a[ j ][ i ];
最后，显示矩阵 t 的元素。

解决方案

Python

#Initialize matrix a
a = [
        [1, 2, 3],
        [4, 5, 6],
        [7, 8, 9]
    ];
 
#Calculates number of rows and columns present in given matrix
rows = len(a);
cols = len(a[0]);
 
#Declare array t with reverse dimensions and is initialized with zeroes.
t = [[0]*rows for i in range(cols)];
 
#Calculates transpose of given matrix
for i in range(0, cols):
    for j in range(0, rows):
        #Converts the row of original matrix into column of transposed matrix
        t[i][j] = a[j][i];
 
print("Transpose of given matrix: ");
for i in range(0, cols):
    for j in range(0, rows):
        print(t[i][j]),
 
    print(" ");

输出

Transpose of given matrix: 
1 4 7 
2 5 8 
3 6 9

C

#include <stdio.h>
 
int main()
{
    int rows, cols;
        
    //Initialize matrix a
    int a[][3] = {
                    {1, 2, 3},
                    {4, 5, 6},
                    {7, 8, 9}
                };
    
    //Calculates number of rows and columns present in given matrix
    rows = (sizeof(a)/sizeof(a[0]));
    cols = (sizeof(a)/sizeof(a[0][0]))/rows;
    
    //Declare array t with reverse dimensions
    int t[cols][rows];
    
    //Calculates transpose of given matrix
    for(int i = 0; i < cols; i++){
        for(int j = 0; j < rows; j++){
            //Converts the row of original matrix into column of transposed matrix
            t[i][j] = a[j][i];
        }
    }
    
    printf("Transpose of given matrix: \n");
    for(int i = 0; i < cols; i++){
        for(int j = 0; j < rows; j++){
           printf("%d ", t[i][j]);
        }
        printf("\n");
    }
 
    return 0;
}

输出

Transpose of given matrix: 
1 4 7 
2 5 8 
3 6 9

JAVA

public class Transpose
{
    public static void main(String[] args) {
        int rows, cols;
        
        //Initialize matrix a
          int a[][] = {
                          {1, 2, 3},
                          {4, 5, 6},
                          {7, 8, 9}
                       };
          
          //Calculates number of rows and columns present in given matrix
          rows = a.length;
        cols = a[0].length;
        
        //Declare array t with reverse dimensions
        int t[][] = new int[cols][rows];
        
        //Calculates transpose of given matrix
        for(int i = 0; i < cols; i++){
            for(int j = 0; j < rows; j++){
                //Converts the row of original matrix into column of transposed matrix
                t[i][j] = a[j][i];
            }
        }
        
        System.out.println("Transpose of given matrix: ");
        for(int i = 0; i < cols; i++){
            for(int j = 0; j < rows; j++){
               System.out.print(t[i][j] + " ");
            }
            System.out.println();
        }
    }
}

输出

Transpose of given matrix: 
1 4 7 
2 5 8 
3 6 9

C#

using System;
                    
public class Transpose
{
    public static void Main()
    {
        int rows, cols;
        
        //Initialize matrix a
          int[,] a = {
                          {1, 2, 3},
                          {4, 5, 6},
                          {7, 8, 9}
                     };
          
          //Calculates number of rows and columns present in given matrix
          rows = a.GetLength(0);
        cols = a.GetLength(1);
        
        //Declare array t with reverse dimensions
        int[,] t = new int[cols,rows];
        
        //Calculates transpose of given matrix
        for(int i = 0; i < cols; i++){
            for(int j = 0; j < rows; j++){
                //Converts the row of original matrix into column of transposed matrix
                t[i,j] = a[j,i];
            }
        }
        
        Console.WriteLine("Transpose of given matrix: ");
        for(int i = 0; i < cols; i++){
            for(int j = 0; j < rows; j++){
               Console.Write(t[i,j] + " ");
            }
            Console.WriteLine();
        }
    }
}

输出

Transpose of given matrix: 
1 4 7 
2 5 8 
3 6 9

PHP

<!DOCTYPE html>
<html>
<body>
<?php
//Initialize matrix a
$a = array(
            array(1, 2, 3),
            array(4, 5, 6),
            array(7, 8, 9)
           );
 
//Calculates number of rows and columns present in given matrix
$rows = count($a);
$cols = count($a[0]);
 
//Declare array t with reverse dimensions and initialize it with 0
$t = array_fill(0, $cols, array_fill(0, $rows, 0));
 
//Calculates transpose of given matrix
for($i = 0; $i < $cols; $i++){
    for($j = 0; $j < $rows; $j++){
        //Converts the row of original matrix into column of transposed matrix
        $t[$i][$j] = $a[$j][$i];
    }
}
 
print("Transpose of given matrix: <br>");
for($i = 0; $i < $cols; $i++){
    for($j = 0; $j < $rows; $j++){
       print($t[$i][$j] . " ");
    }
    print("<br>");
}
?>
</body>
</html>

输出

Transpose of given matrix: 
1 4 7 
2 5 8 
3 6 9

下一主题#

查找给定矩阵的转置的程序

说明

矩阵的转置

算法

解决方案

Python

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JAVA

C#

PHP

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程序

查找给定矩阵的转置的程序

说明

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