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Code Matrix

Program to check idempotent matrix

An idempotent matrix is a square matrix that remains unchanged when multiplied by itself. In other words, if matrix A is idempotent, then A^2 = A. The term "idempotent" comes from the Greek word "idem," which means "the same." Thus, an idempotent matrix is one that is the same as itself after being multiplied by itself.

A check for idempotent matrix involves verifying whether the matrix satisfies the definition of an idempotent matrix. To check if a matrix A is idempotent, you need to multiply it by itself (i.e., A^2) and then compare the result to the original matrix A. If the two matrices are the same, then A is an idempotent matrix. In mathematical terms, this can be expressed as:

A^2 = A

Here are the steps to check if a matrix is idempotent:

  1. Multiply the matrix A by itself: A^2 = A × A
  2. Compare the resulting matrix A^2 with the original matrix A.
  3. If A^2 = A, then the matrix A is idempotent.

Example

The matrix [
[3, -6, 0],
[1, -2, 0],
[0, 0, 1]
] is idempotent ?.

To check this, we need to compute the matrix multiplication A^2, where A is the given matrix:

A^2 = [
[3, -6, 0],
[1, -2, 0],
[0, 0, 1]
] × [
[3, -6, 0],
[1, -2, 0],
[0, 0, 1]
]

Simplifying the multiplication, we get:

A^2 = [
[9, -18, 0],
[3, -6, 0],
[0, 0, 1]
]

Now, we need to compare A^2 with A:

A = [
[3, -6, 0],
[1, -2, 0],
[0, 0, 1]
]

A^2 = [
[9, -18, 0],
[3, -6, 0],
[0, 0, 1]
]

Since A^2 is equal to A, the matrix is idempotent.

Code Solution

/*
  C Program 
+ Program to check idempotent matrix
*/
#include <stdio.h>

#define ROW 3
#define COL 3

//Display the element of given 2d matrix
void show_data(int matrix[][COL]) {
  
  printf("-----------------\n");
  
  for (int i = 0; i < ROW; ++i) {

    for (int j = 0; j < COL; ++j) {

      printf("%4d", matrix[i][j]);
    }

    printf("\n");
  }

  printf("\n");
}
void is_idempotent(int matrix[][COL])
{

  //This matrix are store the result of multiplication 
  int result[ROW][COL];

  for (int i = 0; i < ROW; ++i) {

    for (int j = 0; j < COL; ++j) {

      //Set the initial value of new matrix element
      result[i][j] = 0;

      for (int k = 0; k < ROW; ++k) {

        //Multiply matrix A [i] row and [k] columns to the Matrix B [k] columns and [j] rows
        result[i][j] += matrix[i][k] * matrix[k][j];
      }
    }
  }
  //Display Matrix Elements
  printf("  Matrix \n");
  //print element of matrix
  show_data(matrix);
  

  for (int i = 0; i < ROW; ++i) {

    for (int j = 0; j < COL; ++j) 
    {
      //Compare two matrix element    
      if(matrix[i][j]!=result[i][j])
      {

        printf("Matrix is not idempotent\n");
        return;
      }
    }
  }
  printf("Matrix is idempotent\n");
}
int main() {
  //Define matrix 
  int matrix[ROW][COL] = {
    {
      3, -6, 0
    },

    {
      1, -2, 0
    },
    {
      0,  0, 1
    }
  };
  is_idempotent(matrix);
  
  return 0;
}

Output

  Matrix
-----------------
   3  -6   0
   1  -2   0
   0   0   1

Matrix is idempotent
/*
  C++ Program
  Program to check idempotent matrix
*/
#include<iostream>
#define ROW 3
#define COL 3
using namespace std;


class MyMatrix {
	public:

		//Display the element of given 2d matrix
		void show_data(int matrix[][COL]) {
		
			cout << "-----------------\n";
			for (int i = 0; i < ROW; ++i) {
				for (int j = 0; j < COL; ++j) {
					cout << " " << matrix[i][j];
				}
				cout << "\n";
			}
			cout << "\n";
		}
	void is_idempotent(int matrix[][COL]) {
		
		int result[ROW][COL];
		for (int i = 0; i < ROW; ++i) {
			for (int j = 0; j < COL; ++j) {
				//Set the initial value of new matrix element
				result[i][j] = 0;
				for (int k = 0; k < ROW; ++k) {
					//Multiply matrix A [i] row and [k] columns to the Matrix B [k] columns and [j] rows
					result[i][j] += matrix[i][k] *matrix[k][j];
				}
			}
		}
		//Display Matrix Elements

		cout << " Matrix \n";
		//print element of matrix
		this->show_data(matrix);
		for (int i = 0; i < ROW; ++i) {
			for (int j = 0; j < COL; ++j) {
				//Compare two matrix element    

				if (matrix[i][j] != result[i][j]) {
					cout << "Matrix is not idempotent\n";
					return;
				}
			}
		}
		cout << "Matrix is idempotent\n";
	}
};
int main() {
	MyMatrix obj ;
	int matrix[][COL] = {
		{
			3,
			-6,
			0
		},
		{
			1,
			-2,
			0
		},
		{
			0,
			0,
			1
		}
	};
	obj.is_idempotent(matrix);
	return 0;
}

Output

 Matrix
-----------------
 3 -6 0
 1 -2 0
 0 0 1

Matrix is idempotent
/*
  Java Program
  Program to check idempotent matrix
*/

public class MyMatrix {

  //Display the element of given 2d matrix
  public void show_data(int [][] matrix) {
    int row = matrix.length;
    int col = matrix[0].length; 
    System.out.print("-----------------\n");
    
    for (int i = 0; i < row; ++i) {

      for (int j = 0; j < col; ++j) {

        System.out.print("  "+ matrix[i][j]);
      }

      System.out.print("\n");
    }

    System.out.print("\n");
  }
  public void is_idempotent(int [][] matrix)
  {
    int row = matrix.length;
    int col = matrix[0].length; 
    //This matrix are store the result of multiplication 
    int [][]result= new int[row][col];

    for (int i = 0; i < row; ++i) {

      for (int j = 0; j < col; ++j) {

        //Set the initial value of new matrix element
        result[i][j] = 0;

        for (int k = 0; k < row; ++k) {

          //Multiply matrix A [i] row and [k] columns to the Matrix B [k] columns and [j] rows
          result[i][j] += matrix[i][k] * matrix[k][j];
        }
      }
    }
    //Display Matrix Elements
    System.out.print("  Matrix \n");
    //print element of matrix
    show_data(matrix);
    

    for (int i = 0; i < row; ++i) {

      for (int j = 0; j < col; ++j) 
      {
        //Compare two matrix element    
        if(matrix[i][j]!=result[i][j])
        {

          System.out.print("Matrix is not idempotent\n");
          return;
        }
      }
    }
    System.out.print("Matrix is idempotent\n");
  }
  public static void main(String[] args) {
    
    MyMatrix obj = new MyMatrix();
    
    int[][] matrix = {
      {
        3, -6, 0
      },

      {
        1, -2, 0
      },
      {
        0,  0, 1
      }
    };
    
  
    obj.is_idempotent(matrix);
   
  }
}

Output

 Matrix
-----------------
 3 -6 0
 1 -2 0
 0 0 1

Matrix is idempotent
using System;

/*
  C# Program
  Program to check idempotent matrix
*/

public class MyMatrix {
	//Display the element of given 2d matrix
	public void show_data(int[,] matrix) {
		int row = matrix.GetLength(0);
		int col = matrix.GetLength(1);
		Console.Write("-----------------\n");
		for (int i = 0; i < row; ++i) {
			for (int j = 0; j < col; ++j) {
				Console.Write(" " + matrix[i,j]);
			}
			Console.Write("\n");
		}
		Console.Write("\n");
	}
	public void is_idempotent(int[,] matrix) {
		int row = matrix.GetLength(0);
		int col = matrix.GetLength(1);
		
		//This matrix are store the result of multiplication 
		int[,] result = new int[row,col];
		for (int i = 0; i < row; ++i) {
			for (int j = 0; j < col; ++j) {
				//Set the initial value of new matrix element
				result[i,j] = 0;
				for (int k = 0; k < row; ++k) {
					//Multiply matrix A [i] row and [k] columns to the Matrix B [k] columns and [j] rows
					result[i,j] += matrix[i,k] * matrix[k,j];
				}
			}
		}
		Console.Write(" Matrix \n");
		show_data(matrix);
		for (int i = 0; i < row; ++i) {
			for (int j = 0; j < col; ++j) {
				//Compare two matrix element    

				if (matrix[i,j] != result[i,j]) {
					Console.Write("Matrix is not idempotent\n");
					return;
				}
			}
		}
		Console.Write("Matrix is idempotent\n");
	}
	public static void Main(String[] args) {
		MyMatrix obj = new MyMatrix();
		int[,] matrix = {
			{
				3,
				-6,
				0
			},
			{
				1,
				-2,
				0
			},
			{
				0,
				0,
				1
			}
		};
		obj.is_idempotent(matrix);
	}
}

Output

 Matrix
-----------------
 3 -6 0
 1 -2 0
 0 0 1

Matrix is idempotent
<?php
/*
  Php Program
  Program to check idempotent matrix
*/
class MyMatrix {
	//Display the element of given 2d matrix

	public 	function show_data($matrix) {
		$row = count($matrix);
		$col = count($matrix[0]);
		echo("-----------------\n");
		for ($i = 0; $i < $row; ++$i) {
			for ($j = 0; $j < $col; ++$j) {
				echo(" ". $matrix[$i][$j]);
			}
			echo("\n");
		}
		echo("\n");
	}
	public 	function is_idempotent($matrix) {
		$row = count($matrix);
		$col = count($matrix[0]);
		//This matrix are store the result of multiplication 
		$result = array_fill(0, $row, array_fill(0, $col, 0));
		for ($i = 0; $i < $row; ++$i) {
			for ($j = 0; $j < $col; ++$j) {
				//Set the initial value of new matrix element
				$result[$i][$j] = 0;
				for ($k = 0; $k < $row; ++$k) {
					//Multiply matrix A [i] row and [k] columns to the Matrix B [k] columns and [j] rows
					$result[$i][$j] += $matrix[$i][$k] *$matrix[$k][$j];
				}
			}
		}
		//Display Matrix Elements

		echo(" Matrix \n");
		//print element of matrix
		$this->show_data($matrix);
		for ($i = 0; $i < $row; ++$i) {
			for ($j = 0; $j < $col; ++$j) {
				//Compare two matrix element    

				if ($matrix[$i][$j] != $result[$i][$j]) {
					echo("Matrix is not idempotent\n");
					return;
				}
			}
		}
		echo("Matrix is idempotent\n");
	}
}

function main() {
	$obj = new MyMatrix();
	$matrix = array(array(3, -6, 0), array(1, -2, 0), array(0, 0, 1));
	$obj->is_idempotent($matrix);

}
main();

Output

 Matrix
-----------------
 3 -6 0
 1 -2 0
 0 0 1

Matrix is idempotent
/*
  Node Js Program
  Program to check idempotent matrix
*/
class MyMatrix {
	//Display the element of given 2d matrix
	show_data(matrix) {
		var row = matrix.length;
		var col = matrix[0].length;
		process.stdout.write("-----------------\n");
		for (var i = 0; i < row; ++i) {
			for (var j = 0; j < col; ++j) {
				process.stdout.write(" " + matrix[i][j]);
			}

			process.stdout.write("\n");
		}

		process.stdout.write("\n");
	}
	is_idempotent(matrix) {
		var row = matrix.length;
		var col = matrix[0].length;
		//This matrix are store the result of multiplication 
		var result = Array(row).fill(0).map(() => new Array(col).fill(0));
		for (var i = 0; i < row; ++i) {
			for (var j = 0; j < col; ++j) {
				//Set the initial value of new matrix element
				result[i][j] = 0;
				for (var k = 0; k < row; ++k) {
					//Multiply matrix A [i] row and [k] columns to the Matrix B [k] columns and [j] rows
					result[i][j] += matrix[i][k] *matrix[k][j];
				}
			}
		}

		//Display Matrix Elements

		process.stdout.write(" Matrix \n");
		//print element of matrix
		this.show_data(matrix);
		for (var i = 0; i < row; ++i) {
			for (var j = 0; j < col; ++j) {
				//Compare two matrix element    

				if (matrix[i][j] != result[i][j]) {
					process.stdout.write("Matrix is not idempotent\n");
					return;
				}
			}
		}

		process.stdout.write("Matrix is idempotent\n");
	}
}

function main(args) {
	var obj = new MyMatrix();
	var matrix = [
		[3, -6, 0],
		[1, -2, 0],
		[0, 0, 1]
	];
	obj.is_idempotent(matrix);
}

main();

Output

 Matrix
-----------------
 3 -6 0
 1 -2 0
 0 0 1

Matrix is idempotent
# Python 3 Program
# Program to check idempotent matrix
class MyMatrix :
	# Display the element of given 2d matrix
	def show_data(self, matrix) :
		row = len(matrix)
		col = len(matrix[0])
		print("-----------------\n", end = "")
		i = 0
		j = 0
		while (i < row) :
			j = 0
			while (j < col) :
				print(" ", matrix[i][j], end = "")
				j += 1
			
			print("\n", end = "")
			i += 1
		
		print("\n", end = "")
	
	def is_idempotent(self, matrix) :
		row = len(matrix)
		col = len(matrix[0])
		result = [
			[0] * col
			for _ in range(row)
		]
		i = 0
		j = 0
		k = 0
		while (i < row) :
			j = 0
			while (j < col) :
				# Set the initial value of new matrix element
				result[i][j] = 0
				k = 0
				while (k < row) :
					# Multiply matrix A [i] row and [k] columns to the Matrix B [k] columns and [j] rows
					result[i][j] += matrix[i][k] * matrix[k][j]
					k += 1
				
				j += 1
			
			i += 1
		
		print(" Matrix \n", end = "")
		self.show_data(matrix)
		i = 0
		while (i < row) :
			j = 0
			while (j < col) :
				# Compare two matrix element    

				if (matrix[i][j] != result[i][j]) :
					print("Matrix is not idempotent\n", end = "")
					return
				
				j += 1
			
			i += 1
		
		print("Matrix is idempotent\n", end = "")
	

def main() :
	obj = MyMatrix()
	matrix = [
		[3, -6, 0],
		[1, -2, 0],
		[0, 0, 1]
	]
	obj.is_idempotent(matrix)


if __name__ == "__main__":
	main()

Output

 Matrix
-----------------
  3  -6  0
  1  -2  0
  0  0  1

Matrix is idempotent
# Ruby Program
# Program to check idempotent matrix
class MyMatrix 
	# Display the element of given 2d matrix
	def show_data(matrix) 
		row = matrix.length
		col = matrix[0].length
		print("-----------------\n")
		i = 0
		j = 0
		while (i < row) 
			j = 0
			while (j < col) 
				print(" ", matrix[i][j])
				j += 1
			end
			print("\n")
			i += 1
		end
		print("\n")
	end
	def is_idempotent(matrix) 
		row = matrix.length
		col = matrix[0].length
		result = Array.new(row) { Array.new(col, 0) }
		i = 0
		j = 0
		k = 0
		while (i < row) 
			j = 0
			while (j < col) 
				# Set the initial value of new matrix element
				result[i][j] = 0
				k = 0
				while (k < row) 
					# Multiply matrix A [i] row and [k] columns to the Matrix B [k] columns and [j] rows
					result[i][j] += matrix[i][k] * matrix[k][j]
					k += 1
				end
				j += 1
			end
			i += 1
		end
		print(" Matrix \n")
		self.show_data(matrix)
		i = 0
		while (i < row) 
			j = 0
			while (j < col) 
				# Compare two matrix element    

				if (matrix[i][j] != result[i][j]) 
					print("Matrix is not idempotent\n")
					return
				end
				j += 1
			end
			i += 1
		end
		print("Matrix is idempotent\n")
	end
end
def main() 
	obj = MyMatrix.new()
	matrix = [
		[3, -6, 0],
		[1, -2, 0],
		[0, 0, 1]
	]
	obj.is_idempotent(matrix)
end
main()

Output

 Matrix 
-----------------
 3 -6 0
 1 -2 0
 0 0 1

Matrix is idempotent

/*
  Scala Program
  Program to check idempotent matrix
*/
class MyMatrix {
	//Display the element of given 2d matrix
	def show_data(matrix: Array[Array[Int]]): Unit = {
		val row: Int = matrix.length;
		val col: Int = matrix(0).length;
		print("-----------------\n");
		var i: Int = 0;
		var j: Int = 0;
		while (i < row) {
			j = 0;
			while (j < col) {
				print(" " + matrix(i)(j));
				j += 1;
			}
			print("\n");
			i += 1;
		}
		print("\n");
	}
	def is_idempotent(matrix: Array[Array[Int]]): Unit = {
		val row: Int = matrix.length;
		val col: Int = matrix(0).length;
		var result: Array[Array[Int]] = Array.fill[Int](row, col)(0);
		var i: Int = 0;
		var j: Int = 0;
		var k: Int = 0;
		while (i < row) {
			j = 0;
			while (j < col) {
				//Set the initial value of new matrix element
				result(i)(j) = 0;
				k = 0;
				while (k < row) {
					//Multiply matrix A [i] row and [k] columns to the Matrix B [k] columns and [j] rows
					result(i)(j) += matrix(i)(k) * matrix(k)(j);
					k += 1;
				}
				j += 1;
			}
			i += 1;
		}
		print(" Matrix \n");
		this.show_data(matrix);
		i = 0;
		while (i < row) {
			j = 0;
			while (j < col) {
				//Compare two matrix element    

				if (matrix(i)(j) != result(i)(j)) {
					print("Matrix is not idempotent\n");

					return;
				}
				j += 1;
			}
			i += 1;
		}
		print("Matrix is idempotent\n");
	}
}
object Main {
	def main(args: Array[String]): Unit = {
		val obj: MyMatrix = new MyMatrix();
		val matrix: Array[Array[Int]] = Array(
			Array(3, -6, 0),
			Array(1, -2, 0),
			Array(0, 0, 1));
		obj.is_idempotent(matrix);
	}
}

Output

 Matrix
-----------------
 3 -6 0
 1 -2 0
 0 0 1

Matrix is idempotent
/*
  Swift Program
  Program to check idempotent matrix
*/
class MyMatrix {
	//Display the element of given 2d matrix
	func show_data(_ matrix: [
		[Int]
	]) {
		let row: Int = matrix.count;
		let col: Int = matrix[0].count;
		print("-----------------\n", terminator: "");
		var i: Int = 0;
		var j: Int = 0;
		while (i < row) {
			j = 0;
			while (j < col) {
				print(" ", matrix[i][j], terminator: "");
				j += 1;
			}
			print("\n", terminator: "");
			i += 1;
		}
		print("\n", terminator: "");
	}
	func is_idempotent(_ matrix: [
		[Int]
	]) {
		let row: Int = matrix.count;
		let col: Int = matrix[0].count;
		var result: [
			[Int]
		] = Array(repeating: Array(repeating: 0, count: col), count: row);
		var i: Int = 0;
		var j: Int = 0;
		var k: Int = 0;
		while (i < row) {
			j = 0;
			while (j < col) {
				//Set the initial value of new matrix element
				result[i][j] = 0;
				k = 0;
				while (k < row) {
					//Multiply matrix A [i] row and [k] columns to the Matrix B [k] columns and [j] rows
					result[i][j] += matrix[i][k] * matrix[k][j];
					k += 1;
				}
				j += 1;
			}
			i += 1;
		}
		print(" Matrix \n", terminator: "");
		self.show_data(matrix);
		i = 0;
		while (i < row) {
			j = 0;
			while (j < col) {
				//Compare two matrix element    

				if (matrix[i][j] != result[i][j]) {
					print("Matrix is not idempotent\n", terminator: "");
					return;
				}
				j += 1;
			}
			i += 1;
		}
		print("Matrix is idempotent\n", terminator: "");
	}
}
func main() {
	let obj: MyMatrix = MyMatrix();
	let matrix: [
		[Int]
	] = [
		[3, -6, 0],
		[1, -2, 0],
		[0, 0, 1]
	];
	obj.is_idempotent(matrix);
}
main();

Output

 Matrix
-----------------
  3  -6  0
  1  -2  0
  0  0  1

Matrix is idempotent

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