Basic Operations on Matrices in C++

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Basic Operations on Matrices in C++

Matrix: A matrix(singular of matrices) in mathematical terms is simply an arrangement of numbers in a definite number of rows and columns.

Few examples of a matrix are as follows:

Matrix Dimensions: The dimensions of a matrix also known as the Order of a matrix gives the exact size of the matrix i.e. the number of elements a matrix can store. The dimensions of a matrix are represented by (N x M); where N and M are the number of rows and the number of columns of the matrix respectively.

Hence, the size of a matrix is equal to the product of N (number of rows) and M (number of columns).

The most common and basic mathematical operations on matrices are as follows:

  • Taking Inputs for the matrix elements and storing them in the matrix.
  • Taking transpose of a matrix and storing it in a new matrix.
  • Addition of two matrices and storing the sum in a new matrix.
  • Subtraction of two matrices and storing the difference in a new matrix.
  • Multiplication of two matrices and storing the product in a new matrix.
  • Calculating Trace of a matrix i.e the sum of the principal diagonal elements of a square matrix [a square matrix is a matrix for which N (number of rows) = M (number of columns)].

Now Let’s dive into the actual coding/programming in C++ to perform these mathematical operations on matrices.

Taking Input for a Matrix

#include <iostream>
  
using namespace std;
  
 int main()
 {
     int N, M;
     
     // Taking input for the order of a matrix 
     cout<<"Enter the order of the matrix:"<<endl;
     cin>>N>>M;
     
     // Defining a matrix variable
     int A[N][M];
     
     // Taking input for the elements of the matrix in the matrix form
     cout<<"Enter Matrix elements:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
             cin>>A[i][j];
         }
     
     // Printing the input matrix
     cout<<"Input Matrix:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
                 cout<<A[i][j]<<" ";
             cout<<endl;
         }

     return 0;
 } 

Output:

Enter the order of the matrix:
3 3
Enter Matrix elements:
4 5 6
3 5 7
7 9 1
Input Matrix:
4 5 6
3 5 7
7 9 1

Also Read Types of Looping statements in C/C++

Transpose of a Matrix (AT)

Transpose of a matrix is defined as the matrix obtained by interchanging the rows of the matrix with the columns of that matrix.

For finding the transpose of a matrix, that matrix need not to be a square matrix.

#include <iostream>
  
using namespace std;
  
 int main()
 {
     int N, M;
     
     // Taking input for the order of matrix A
     cout<<"Enter the order of the matrix:"<<endl;
     cin>>N>>M;
     
     // Defining a matrix variables
     int A[N][M], T[M][N];
     
     // Taking input for the elements of the matrix
     cout<<"Enter Matrix elements:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
             cin>>A[i][j];
         }

 // Calculating transpose of matrix A
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
             T[j][i] = A[i][j];
         }

     // Printing the transpose of the matrix
     cout<<"Transpose of Matrix:"<<endl;
     for(int i = 0; i < M; i++)
         {
             for(int j = 0; j < N; j++)
                 cout<<T[i][j]<<" ";
             cout<<endl;
         }

     return 0;
 } 

Output:

Enter the order of the matrix:
3 4
Enter Matrix elements:
5 6 7 1
5 7 2 3
6 7 4 3
Transpose of Matrix:
5 5 6
6 7 7
7 2 4
1 3 3

Also Read Five Ways to Calculate Power in C++

Adding Two Matrices (A + B)

To perform the addition over two matrices, the two matrices should have the same number of rows and columns.

To add matrix A with matrix B, we have to take the element-wise addition of the corresponding elements of the two matrices.

#include <iostream>

using namespace std;
  
 int main()
 {
     int N, M;
     
     // Taking input for the order of matrices
     cout<<"Enter the order of matrices:"<<endl;
     cin>>N>>M;
     
     // Defining matrix variables
     int A[N][M], B[N][M], C[N][M];
     
     // Taking input for the elements of matrix A
     cout<<"Enter elements of Matrix A:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
             cin>>A[i][j];
         }

     // Taking input for the elements of matrix B         
     cout<<"Enter elements of Matrix B:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
             cin>>B[i][j];
         }
         
     // Calculating the sum of matrices
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
             C[i][j] = A[i][j] + B[i][j];
         }
     
     // Printing the sum of matrices A and B
     cout<<"Sum of Matrix A and B:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
                 cout<<C[i][j]<<" ";
             cout<<endl;
         }
         
     return 0;
 } 

Output:

Enter the order of matrices:
3 3
Enter elements of Matrix A:
2 3 4
5 6 7
2 3 4
Enter elements of Matrix B:
6 7 8
3 6 4
3 4 2
Sum of Matrix A and B:
8 10 12
8 12 11
5 7 6

Subtracting Two Matrices (A – B)

To perform the subtraction over two matrices, the two matrices should have the same number of rows and columns.

To subtract matrix B from matrix A, we have to take the element-wise difference of the corresponding elements of the two matrices.

#include <iostream>
  
using namespace std;
  
 int main()
 {
     int N, M;
     
     // Taking input for the order of matrices 
     cout<<"Enter the order of matrices:"<<endl;
     cin>>N>>M;
     
     // Defining matrix variables
     int A[N][M], B[N][M], C[N][M];
     
     // Taking input for the elements of matrix A
     cout<<"Enter elements of Matrix A:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
             cin>>A[i][j];
         }
         
     // Taking input for the elements of matrix B
     cout<<"Enter elements of Matrix B:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
             cin>>B[i][j];
         }
         
     // Calculating the difference of matrices
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
             C[i][j] = A[i][j] - B[i][j];
         }
     
     // Printing the difference of matrix A and B
     cout<<"Difference of Matrix A and B:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
                 cout<<C[i][j]<<" ";
             cout<<endl;
         }
         
     return 0;
 } 

Output:

Enter the order of matrices:
3 5
Enter elements of Matrix A:
1 2 3 4 5
4 6 7 8 8
2 3 5 3 6
Enter elements of Matrix B:
5 6 2 4 5
7 8 4 2 1
6 8 4 4 2
Difference of Matrix A and B:
-4 -4 1 0 0
-3 -2 3 6 7
-4 -5 1-1 4

Multiplication of Two Matrices (A x B)

We can multiply two matrices only when the number of columns in matrix A is equal to the number of rows in matrix B i.e. If A is of order (N x M) and B is of order (P x Q) then product A x B is possible only when (M = P) and the order of the product matrix will be (N x Q).

#include <iostream>
  
using namespace std;
  
 int main()
 {
     int N, M, P, Q;
     
     // Taking input for the order of matrices
     cout<<"Enter the order of matrix A:"<<endl;
     cin>>N>>M;
     cout<<"Enter the order of matrix B:"<<endl;
     cin>>P>>Q;
     
     // Defining matrix variables
     int A[N][M], B[P][Q], C[N][Q];
     
     // Taking input for the elements of matrix A and B
     cout<<"Enter elements of Matrix A:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < M; j++)
             cin>>A[i][j];
         }
         
     cout<<"Enter elements of Matrix B:"<<endl;
     for(int i = 0; i < P; i++)
         {
             for(int j = 0; j < Q; j++)
             cin>>B[i][j];
         }
         
     // Calculating the product of matrices
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < Q; j++)
                 {
                     C[i][j] = 0;
                     for(int k = 0; k < M; k++ )
                         C[i][j] = C[i][j] + (A[i][k] * B[k][j]);
                 }
         }
     
     // Printing the product of matrix A and B
     cout<<"Product of Matrix A and B:"<<endl;
     for(int i = 0; i < N; i++)
         {
             for(int j = 0; j < Q; j++)
                 cout<<C[i][j]<<" ";
             cout<<endl;
         }
         
     return 0;
 } 

Output:

Enter the order of matrix A:
2 3
Enter the order of matrix B:
3 3
Enter elements of Matrix A:
1 1 4
1 2 3
Enter elements of Matrix B:
1 2 3
4 5 6
7 8 9
Product of Matrix A and B:
33 39 45
30 36 42

Trace of a Matrix (tr(A))

Trace of a square matrix is defined as the sum of the principal diagonal elements of that matrix.

For finding the trace of a matrix, that matrix needs to be a square matrix.

#include <iostream>
   
using namespace std;
   
  int main()
  {
      int N, M;
      
      // Taking input for the order of matrix A
      cout<<"Enter the order of the matrix:"<<endl;
      cin>>N>>M;
      
      // Defining a matrix variable
      int A[N][M], trace = 0;
      
      // Taking input for the elements of the matrix
      cout<<"Enter Matrix elements:"<<endl;
      for(int i = 0; i < N; i++)
          {
              for(int j = 0; j < M; j++)
              cin>>A[i][j];
          }
  
  // Calculating trace of matrix A
      for(int i = 0; i < N; i++)
          {
              for(int j = 0; j < M; j++)
                 if(i == j)
                     trace = trace + A[i][j];
          }
  
      // Printing the transpose of the matrix
      cout<<"Trace of Matrix A = "<<trace<<endl;
  
      return 0;
  } 

Output:

Enter the order of the matrix:
3 3
Enter Matrix elements:
2 3 5
6 7 4
7 4 9
Trace of Matrix A = 18

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