检查幂等矩阵的程序
给定一个 N * N 矩阵，任务是检查矩阵是否是幂等矩阵。
幂等矩阵： 如果矩阵乘以自身返回相同的矩阵，则称矩阵是幂等矩阵。当且仅当M * M = M时，矩阵 M 被称为幂等矩阵。在幂等矩阵中，M 是一个方阵。
例子：
Input : mat[][] = {{3, -6},
{1, -2}};
Output : Idempotent Matrix
Input : mat[N][N] = {{2, -2, -4},
{-1, 3, 4},
{1, -2, -3}}
Output : Idempotent Matrix.C++
// Program to check given matrix
// is idempotent matrix or not.
#include
#define N 3
using namespace std;
// Function for matrix multiplication.
void multiply(int mat[][N], int res[][N])
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
res[i][j] = 0;
for (int k = 0; k < N; k++)
res[i][j] += mat[i][k] * mat[k][j];
}
}
}
// Function to check idempotent
// property of matrix.
bool checkIdempotent(int mat[][N])
{
// Calculate multiplication of matrix
// with itself and store it into res.
int res[N][N];
multiply(mat, res);
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
if (mat[i][j] != res[i][j])
return false;
return true;
}
// Driver function.
int main()
{
int mat[N][N] = {{2, -2, -4},
{-1, 3, 4},
{1, -2, -3}};
// checkIdempotent function call.
if (checkIdempotent(mat))
cout << "Idempotent Matrix";
else
cout << "Not Idempotent Matrix.";
return 0;
} Java
// Java program to check given matrix
// is idempotent matrix or not.
import java.io.*;
class GFG
{
static int N = 3;
// Function for matrix multiplication.
static void multiply(int mat[][], int res[][])
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
res[i][j] = 0;
for (int k = 0; k < N; k++)
res[i][j] += mat[i][k] * mat[k][j];
}
}
}
// Function to check idempotent
// property of matrix.
static boolean checkIdempotent(int mat[][])
{
// Calculate multiplication of matrix
// with itself and store it into res.
int res[][] = new int[N][N];
multiply(mat, res);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
if (mat[i][j] != res[i][j])
return false;
}
}
return true;
}
// Driver code.
public static void main (String[] args)
{
int mat[][] = {{2, -2, -4},
{-1, 3, 4},
{1, -2, -3}};
// checkIdempotent function call.
if (checkIdempotent(mat))
System.out.println( "Idempotent Matrix");
else
System.out.println("Not Idempotent Matrix.");
}
}
// This code is contributed by vt_m.Python 3
# Python Program to check given matrix
# is idempotent matrix or not.
import math
# Function for matrix multiplication.
def multiply(mat, res):
N= len(mat)
for i in range(0,N):
for j in range(0,N):
res[i][j] = 0
for k in range(0,N):
res[i][j] += mat[i][k] * mat[k][j]
# Function to check idempotent
# property of matrix.
def checkIdempotent(mat):
N= len(mat)
# Calculate multiplication of matrix
# with itself and store it into res.
res =[[0]*N for i in range(0,N)]
multiply(mat, res)
for i in range(0,N):
for j in range(0,N):
if (mat[i][j] != res[i][j]):
return False
return True
# driver Function
mat = [ [2, -2, -4],
[-1, 3, 4],
[1, -2, -3] ]
# checkIdempotent function call.
if (checkIdempotent(mat)):
print("Idempotent Matrix")
else:
print("Not Idempotent Matrix.")
# This code is contributed by Gitanjali.C#
// C# program to check given matrix
// is idempotent matrix or not.
using System;
class GFG
{
static int N = 3;
// Function for matrix multiplication.
static void multiply(int [,]mat, int [,]res)
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
res[i,j] = 0;
for (int k = 0; k < N; k++)
res[i,j] += mat[i,k] * mat[k,j];
}
}
}
// Function to check idempotent
// property of matrix.
static bool checkIdempotent(int [,]mat)
{
// Calculate multiplication of matrix
// with itself and store it into res.
int [,]res = new int[N,N];
multiply(mat, res);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
if (mat[i,j] != res[i,j])
return false;
}
}
return true;
}
// Driver code
public static void Main ()
{
int [,]mat = {{2, -2, 4},
{-1, 3, 4},
{1, -2, -3}};
// checkIdempotent function call.
if (checkIdempotent(mat))
Console.WriteLine( "Idempotent Matrix");
else
Console.WriteLine("Not Idempotent Matrix.");
}
}
// This code is contributed by vt_m.Javascript
输出
Idempotent Matrix