eigen_valuein_.cpp maths

#include<bits/stdc++.h>
using namespace std;


int calculateDeterminant(int** arr, int rows, int cols) {
    // Base case: If the matrix is 1x1, return its only element
    if (rows == 1 && cols == 1) {
        return arr[0][0];
    }

    // Initialize the determinant value
    int determinant = 0;

    // Create a temporary submatrix
    int** subMatrix = new int*[rows - 1];
    for (int i = 0; i < rows - 1; ++i) {
        subMatrix[i] = new int[cols - 1];
    }

    // Iterate through the first row to calculate the determinant
    for (int j = 0; j < cols; ++j) {
        // Create the submatrix by excluding the current row and column
        int subRow = 0;
        for (int i = 1; i < rows; ++i) {
            int subCol = 0;
            for (int k = 0; k < cols; ++k) {
                if (k != j) {
                    subMatrix[subRow][subCol] = arr[i][k];
                    subCol++;
                }
            }
            subRow++;
        }

        // Calculate the determinant recursively
        int sign = (j % 2 == 0) ? 1 : -1;  // Alternating signs
        determinant += sign * arr[0][j] * calculateDeterminant(subMatrix, rows - 1, cols - 1);
    }

    // Clean up memory for the submatrix
    for (int i = 0; i < rows - 1; ++i) {
        delete[] subMatrix[i];
    }
    delete[] subMatrix;

    return determinant;
}
int main(){
    int rows,col;
    cout<<"Give the value of X and Y : ";
    cin>>rows>>col;
    int** arr = new int*[rows];
    for (int i = 0; i < rows; i++)
    {
        arr[i] = new int[col];
        for (int j = 0; j < col; j++)
        {
            cin>>arr[i][j];   
        }
        
    }

    
    //initializing the identity matrix ;
    int** id =new int*[rows];
    for (int i = 0; i < rows; i++)
    {
        id[i] =new int[col];
        for (int j = 0; j < col; j++)
        {
            if(i==j){
                id[i][j] = 1;
            }
            else
            {
                id[i][j] =0;
            }
            
        }
        
    }
    
    // A-λI
    cout<<calculateDeterminant(arr,rows,col)<<endl;

    for (int i = 0; i < rows; i++)
    {
        for (int j = 0; j < col; j++)
        {
            arr[i][j] = arr[i][j] - id[i][j];
            
        }
    }
    cout<<endl;
    

    //Printing the  A-λI function
    for (int i = 0; i < rows; i++)
    {
        for (int j = 0; j < col; j++)
        {
            if (i==j)
            {
                cout<<arr[i][j]<<"-λ\t";
            }
            else
            {
                cout<<arr[i][j]<<"\t";
            }
            
            
        }
        cout<<endl;
    }

   
    

    
    for (int i = 0; i < rows; i++) {
    delete[] arr[i]; 
    delete[] id[i];
    }
    delete[] arr; 
    delete[] id;


}