确定给定矩阵是否为单位矩阵的程序

17 Mar 2025 | 4 分钟阅读

说明

在此程序中，我们需要检查给定的矩阵是否为单位矩阵。

单位矩阵

Program to determine whether a given matrix is an identity matrix

当一个矩阵是方阵，主对角线上的元素都是 1，其余元素都是 0 时，该矩阵被称为单位矩阵。

算法

声明并初始化一个二维数组 a。
分别计算数组中的行数和列数，并存储在变量 rows 和 columns 中。
初始化变量 flag 为 true。
检查给定的矩阵是否具有相同的行数和列数（即是否为方阵）。
如果不是，则打印错误消息“矩阵应为方阵。”
如果给定的矩阵是方阵，则遍历该数组，并检查主对角线上的所有元素是否为 1，其余元素是否为 0。
如果任何条件不满足，则将 flag 设置为 false 并中断循环。
如果 flag 等于 true，则表示给定的矩阵是单位矩阵。
否则，给定的矩阵不是单位矩阵。

解决方案

Python

#Initialize matrix a
a = [   
        [1, 0, 0],
        [0, 1, 0],
        [0, 0, 1]
    ];
    
flag = True;
 
#Calculates number of rows and columns present in given matrix
rows = len(a);
cols = len(a[0]);
 
#Checks whether given matrix is a square matrix or not
if(rows != cols):
    print("Matrix should be a square matrix");
 
else:
    #Checks if diagonal elements are equal to 1 and rest of elements are 0
    for i in range(0, rows):
        for j in range(0, cols):
            if(i == j and a[i][j] != 1):
                flag = False;
                break;
                
            if(i != j and a[i][j] != 0):
                flag = False;
                break;
 
    
    if(flag):
        print("Given matrix is an identity matrix");
    else:
        print("Given matrix is not an identity matrix");

输出

Given matrix is an identity matrix

C

#include <stdio.h>
#include <stdbool.h>
 
int main()
{
    int rows, cols;
    bool flag = true;
    
    //Initialize matrix a
    int a[][3] = {   
                    {1, 0, 0},
                    {0, 1, 0},
                    {0, 0, 1}
                };
    
    //Calculates number of rows and columns present in given matrix
    rows = (sizeof(a)/sizeof(a[0]));
    cols = (sizeof(a)/sizeof(a[0][0]))/rows;
    
    //Checks whether given matrix is a square matrix or not
    if(rows != cols){
        printf("Matrix should be a square matrix");
    }
    else{
        //Checks if diagonal elements are equal to 1 and rest of elements are 0
        for(int i = 0; i < rows; i++){
            for(int j = 0; j < cols; j++){
              if(i == j && a[i][j] != 1){
                  flag = false;
                  break;
              }
              if(i != j && a[i][j] != 0){
                  flag = false;
                  break;
              }
            }
        }
        
        if(flag)
            printf("Given matrix is an identity matrix");
        else
            printf("Given matrix is not an identity matrix");
    }    
    return 0;
}

输出

Given matrix is an identity matrix

JAVA

public class IdentityMatrix 
{
    public static void main(String[] args) {
        int rows, cols;
        boolean flag = true;
        
        //Initialize matrix a
        int a[][] = {   
                        {1, 0, 0},
                        {0, 1, 0},
                        {0, 0, 1}
                    };
        
        //Calculates the number of rows and columns present in the given matrix

          rows = a.length;
        cols = a[0].length;
        
        //Checks whether given matrix is a square matrix or not
        if(rows != cols){
            System.out.println("Matrix should be a square matrix");
        }
        else {
            //Checks if diagonal elements are equal to 1 and rest of elements are 0
            for(int i = 0; i < rows; i++){
                for(int j = 0; j < cols; j++){
                  if(i == j && a[i][j] != 1){
                      flag = false;
                      break;
                  }
                  if(i != j && a[i][j] != 0){
                      flag = false;
                      break;
                  }
                }
            }
            
            if(flag)
                System.out.println("Given matrix is an identity matrix");
            else
                System.out.println("Given matrix is not an identity matrix");
        }
    }
}

输出

Given matrix is an identity matrix

C#

using System;
                    
public class IdentityMatrix
{
    public static void Main()
    {
        int rows, cols;
        Boolean flag = true;
        
        //Initialize matrix a
        int[,] a = {   
                        {1, 0, 0},
                        {0, 1, 0},
                        {0, 0, 1}
                   };
        
        //Calculates the number of rows and columns present in the given matrix

          rows = a.GetLength(0);
        cols = a.GetLength(1);
        
        //Checks whether given matrix is a square matrix or not
        if(rows != cols){
            Console.WriteLine("Matrix should be a square matrix");
        }
        else {
            //Checks if diagonal elements are equal to 1 and rest of elements are 0
            for(int i = 0; i < rows; i++){
                for(int j = 0; j < cols; j++){
                  if(i == j && a[i,j] != 1){
                      flag = false;
                      break;
                  }
                  if(i != j && a[i,j] != 0){
                      flag = false;
                      break;
                  }
                }
            }
            
            if(flag)
                Console.WriteLine("Given matrix is an identity matrix");
            else
                Console.WriteLine("Given matrix is not an identity matrix");
        }
    }
}

输出

Given matrix is an identity matrix

PHP

<!DOCTYPE html>
<html>
<body>
<?php
//Initialize matrix a
$a = array(   
            array(1, 0, 0),
            array(0, 1, 0),
            array(0, 0, 1)
          );
 
$flag = true;
    
//Calculates number of rows and columns present in given matrix
$rows = count($a);
$cols = count($a[0]);
 
//Checks whether given matrix is a square matrix or not
if($rows != $cols){
    print("Matrix should be a square matrix <br>");
}
else {
    //Checks if diagonal elements are equal to 1 and rest of elements are 0
    for($i = 0; $i < $rows; $i++){
        for($j = 0; $j < $cols; $j++){
          if($i == $j && $a[$i][$j] != 1){
              $flag = false;
              break;
          }
          if($i != $j && $a[$i][$j] != 0){
              $flag = false;
              break;
          }
        }
    }
    
    if($flag)
        print("Given matrix is an identity matrix <br>");
    else
        print("Given matrix is not an identity matrix <br>");
}
?>
</body>
</html>

输出

Given matrix is an identity matrix

下一主题#

确定给定矩阵是否为单位矩阵的程序

说明

单位矩阵

算法

解决方案

Python

C

JAVA

C#

PHP

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程序

确定给定矩阵是否为单位矩阵的程序

说明

单位矩阵

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解决方案

Python

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JAVA

C#

PHP

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