Matrix operations using operator overloading
Last Updated :
15 Jul, 2025
Pre-requisite: Operator Overloading
Given two matrix mat1[][] and mat2[][] of NxN dimensions, the task is to perform Matrix Operations using Operator Overloading.
Examples:
Input: arr1[][] = { {1, 2, 3}, {4, 5, 6}, {1, 2, 3}}, arr2[][] = { {1, 2, 3}, {4, 5, 16}, {1, 2, 3}}
Output:
Addition of two given Matrices is:
2 4 6
8 10 22
2 4 6
Subtraction of two given Matrices is:
0 0 0
0 0 -10
0 0 0
Multiplication of two given Matrices is:
12 18 44
30 45 110
12 18 44
Input: arr1[][] = { {11, 2, 3}, {4, 5, 0}, {1, 12, 3}}, arr2[][] = { {1, 2, 3}, {41, 5, 16}, {1, 22, 3}}
Output:
Addition of two given Matrices is :
12 4 6
45 10 16
2 34 6
Subtraction of two given Matrices is :
10 0 0
-37 0 -16
0 -10 0
Multiplication of two given Matrices is :
96 98 74
209 33 92
496 128 204
Approach:
To overload +, -, * operators, we will create a class named matrix and then make a public function to overload the operators.
- To overload operator '+' use prototype:
Return_Type classname :: operator +(Argument list)
{
// Function Body
}
Let there are two matrix M1[][] and M2[][] of same dimensions. Using Operator Overloading M1[][] and M2[][] can be added as M1 + M2.
In the above statement M1 is treated as global and M2[][] is passed as an argument to the function "void Matrix::operator+(Matrix x)".
In the above overloaded function, the approach for addition of two matrix is implemented by treating M1[][] as first and M2[][] as second Matrix i.e., Matrix x(as the arguments).
- To overload operator '-' use prototype:
Return_Type classname :: operator -(Argument list)
{
// Function Body
}
Let there are two matrix M1[][] and M2[][] of same dimensions. Using Operator Overloading M1[][] and M2[][] can be added as M1 - M2
In the above statement M1 is treated hai global and M2[][] is passed as an argument to the function "void Matrix::operator-(Matrix x)".
In the above overloaded function, the approach for subtraction of two matrix is implemented by treating M1[][] as first and M2[][] as second Matrix i.e., Matrix x(as the arguments).
- To overload operator '*' use prototype:
Return_Type classname :: operator *(Argument list)
{
// Function Body
}
Let there are two matrix M1[][] and M2[][] of same dimensions. Using Operator Overloading M1[][] and M2[][] can be added as M1 * M2.
In the above statement M1 is treated hai global and M2[][] is passed as an argument to the function "void Matrix::operator*(Matrix x)".
In the above overloaded function, the approach for multiplication of two matrix is implemented by treating M1[][] as first and M2[][] as second Matrix i.e., Matrix x(as the arguments).
Below is the implementation of the above approach:
C++
// C++ program for the above approach
#include "bits/stdc++.h"
#define rows 50
#define cols 50
using namespace std;
int N;
// Class for Matrix operator overloading
class Matrix {
// For input Matrix
int arr[rows][cols];
public:
// Function to take input to arr[][]
void input(vector<vector<int> >& A);
void display();
// Functions for operator overloading
void operator+(Matrix x);
void operator-(Matrix x);
void operator*(Matrix x);
};
// Functions to get input to Matrix
// array arr[][]
void Matrix::input(vector<vector<int> >& A)
{
// Traverse the vector A[][]
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
arr[i][j] = A[i][j];
}
}
}
// Function to display the element
// of Matrix
void Matrix::display()
{
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Print the element
cout << arr[i][j] << ' ';
}
cout << endl;
}
}
// Function for addition of two Matrix
// using operator overloading
void Matrix::operator+(Matrix x)
{
// To store the sum of Matrices
int mat[N][N];
// Traverse the Matrix x
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Add the corresponding
// blocks of Matrices
mat[i][j] = arr[i][j]
+ x.arr[i][j];
}
}
// Display the sum of Matrices
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Print the element
cout << mat[i][j] << ' ';
}
cout << endl;
}
}
// Function for subtraction of two Matrix
// using operator overloading
void Matrix::operator-(Matrix x)
{
// To store the difference of Matrices
int mat[N][N];
// Traverse the Matrix x
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Subtract the corresponding
// blocks of Matrices
mat[i][j] = arr[i][j]
- x.arr[i][j];
}
}
// Display the difference of Matrices
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Print the element
cout << mat[i][j] << ' ';
}
cout << endl;
}
}
// Function for multiplication of
// two Matrix using operator
// overloading
void Matrix::operator*(Matrix x)
{
// To store the multiplication
// of Matrices
int mat[N][N];
// Traverse the Matrix x
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Initialise current block
// with value zero
mat[i][j] = 0;
for (int k = 0; k < N; k++) {
mat[i][j] += arr[i][k]
* (x.arr[k][j]);
}
}
}
// Display the multiplication
// of Matrices
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Print the element
cout << mat[i][j] << ' ';
}
cout << endl;
}
}
// Driver Code
int main()
{
// Dimension of Matrix
N = 3;
vector<vector<int> > arr1
= { { 1, 2, 3 },
{ 4, 5, 6 },
{ 1, 2, 3 } };
vector<vector<int> > arr2
= { { 1, 2, 3 },
{ 4, 5, 16 },
{ 1, 2, 3 } };
// Declare Matrices
Matrix mat1, mat2;
// Take Input to matrix mat1
mat1.input(arr1);
// Take Input to matrix mat2
mat2.input(arr2);
// For addition of matrix
cout << "Addition of two given"
<< " Matrices is : \n";
mat1 + mat2;
// For subtraction of matrix
cout << "Subtraction of two given"
<< " Matrices is : \n";
mat1 - mat2;
// For multiplication of matrix
cout << "Multiplication of two"
<< " given Matrices is : \n";
mat1* mat2;
return 0;
}
import java.util.*;
public class Matrix {
int arr[][];
int N;
// Constructor to initialize
// Matrix object
public Matrix(int n)
{
N = n;
arr = new int[N][N];
}
// Function to take input to arr[][]
void input(List<List<Integer> > A)
{
// Traverse the List A[][]
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
arr[i][j] = A.get(i).get(j);
}
}
}
// Function to display the element of Matrix
void display()
{
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Print the element
System.out.print(arr[i][j] + " ");
}
System.out.println();
}
}
// Function for addition of two Matrix using operator
// overloading
void add(Matrix x)
{
// To store the sum of Matrices
int mat[][] = new int[N][N];
// Traverse the Matrix x
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Add the corresponding blocks of Matrices
mat[i][j] = arr[i][j] + x.arr[i][j];
}
}
// Display the sum of Matrices
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Print the element
System.out.print(mat[i][j] + " ");
}
System.out.println();
}
}
// Function for subtraction of two Matrix using operator
// overloading
void subtract(Matrix x)
{
// To store the difference of Matrices
int mat[][] = new int[N][N];
// Traverse the Matrix x
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Subtract the corresponding blocks of
// Matrices
mat[i][j] = arr[i][j] - x.arr[i][j];
}
}
// Display the difference of Matrices
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Print the element
System.out.print(mat[i][j] + " ");
}
System.out.println();
}
}
// Function for multiplication of two Matrix using
// operator overloading
public void multiply(Matrix x)
{
// To store the multiplication
// of Matrices
int[][] mat = new int[N][N];
// Traverse the Matrix x
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Initialise current block
// with value zero
mat[i][j] = 0;
for (int k = 0; k < N; k++) {
mat[i][j] += arr[i][k] * (x.arr[k][j]);
}
}
}
// Display the multiplication
// of Matrices
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// Print the element
System.out.print(mat[i][j] + " ");
}
System.out.println();
}
}
// Driver Code
public static void main(String[] args)
{
// Dimension of Matrix
int N = 3;
List<List<Integer> > arr1 = Arrays.asList(
Arrays.asList(1, 2, 3), Arrays.asList(4, 5, 6),
Arrays.asList(1, 2, 3));
List<List<Integer> > arr2 = Arrays.asList(
Arrays.asList(1, 2, 3), Arrays.asList(4, 5, 16),
Arrays.asList(1, 2, 3));
// Declare Matrices
Matrix mat1 = new Matrix(N);
Matrix mat2 = new Matrix(N);
// Take Input to matrix mat1
mat1.input(arr1);
// Take Input to matrix mat2
mat2.input(arr2);
// For addition of matrix
System.out.println(
"Addition of two given Matrices is : ");
mat1.add(mat2);
// For subtraction of matrix
System.out.println(
"Subtraction of two given Matrices is : ");
mat1.subtract(mat2);
// For multiplication of matrix
System.out.println(
"Multiplication of two given Matrices is : ");
mat1.multiply(mat2);
}
}
# Python program for the above approach
# Dimension of Matrix
N = 3
rows = 50
cols = 50
# Class for Matrix operator overloading
class Matrix:
def __init__(self):
# For input Matrix
self.arr = [[0 for i in range(cols)] for j in range(rows)]
# Functions to get input to Matrix
# array arr[][]
def input(self, A):
# Traverse the vector A[][]
for i in range(N):
for j in range(N):
self.arr[i][j] = A[i][j]
# Function to display the element
# of Matrix
def display(self):
for i in range(N):
for j in range(N):
# Print the element
print(self.arr[i][j], end=' ')
print()
# Function for addition of two Matrix
# using operator overloading
def __add__(self, x):
# To store the sum of Matrices
mat = [[0 for i in range(N)] for j in range(N)]
for i in range(N):
for j in range(N):
# Add the corresponding
# blocks of Matrices
mat[i][j] = self.arr[i][j] + x.arr[i][j]
# Display the sum of Matrices
for i in range(N):
for j in range(N):
# Print the element
print(mat[i][j], end=' ')
print()
# Function for subtraction of two Matrix
# using operator overloading
def __sub__(self, x):
# To store the difference of Matrices
mat = [[0 for i in range(N)] for j in range(N)]
# Traverse the Matrix x
for i in range(N):
for j in range(N):
# Subtract the corresponding
# blocks of Matrices
mat[i][j] = self.arr[i][j] - x.arr[i][j]
# Display the difference of Matrices
for i in range(N):
for j in range(N):
# Print the element
print(mat[i][j], end=' ')
print()
# Function for multiplication of
# two Matrix using operator
# overloading
def __mul__(self, x):
# To store the multiplication
# of Matrices
mat = [[0 for i in range(N)] for j in range(N)]
# Traverse the Matrix x
for i in range(N):
for j in range(N):
# Initialise current block
# with value zero
mat[i][j] = 0
for k in range(N):
mat[i][j] += self.arr[i][k] * (x.arr[k][j])
# Display the multiplication
# of Matrices
for i in range(N):
for j in range(N):
# Print the element
print(mat[i][j], end=' ')
print()
# Driver Code
arr1 = [[1, 2, 3],
[4, 5, 6],
[1, 2, 3]]
arr2 = [[1, 2, 3],
[4, 5, 16],
[1, 2, 3]]
# Declare Matrices
mat1 = Matrix()
mat2 = Matrix()
# Take Input to matrix mat1
mat1.input(arr1)
# Take Input to matrix mat2
mat2.input(arr2)
# For addition of matrix
print("Addition of two given Matrices is : ")
mat1 + mat2
# For subtraction of matrix
print("Subtraction of two given Matrices is : ")
mat1 - mat2
# For multiplication of matrix
print("Multiplication of two given Matrices is : ")
mat1 * mat2
function matrixAddition(matrix1, matrix2) {
var result = [];
for (var i = 0; i < matrix1.length; i++) {
var row = [];
for (var j = 0; j < matrix1[i].length; j++) {
row.push(matrix1[i][j] + matrix2[i][j]);
}
result.push(row.join(" "));
}
return result.join("\n");
}
function matrixSubtraction(matrix1, matrix2) {
var result = [];
for (var i = 0; i < matrix1.length; i++) {
var row = [];
for (var j = 0; j < matrix1[i].length; j++) {
row.push(matrix1[i][j] - matrix2[i][j]);
}
result.push(row.join(" "));
}
return result.join("\n");
}
function matrixMultiplication(matrix1, matrix2) {
var result = [];
for (var i = 0; i < matrix1.length; i++) {
var row = [];
for (var j = 0; j < matrix2[0].length; j++) {
var sum = 0;
for (var k = 0; k < matrix1[0].length; k++) {
sum += matrix1[i][k] * matrix2[k][j];
}
row.push(sum);
}
result.push(row.join(" "));
}
return result.join("\n");
}
var matrix1 = [
[1, 2, 3],
[4, 5, 6],
[1, 2, 3]
];
var matrix2 = [
[1, 2, 3],
[4, 5, 16],
[1, 2, 3]
];
console.log("Addition of two given Matrices is: ");
console.log(matrixAddition(matrix1, matrix2));
console.log("\n");
console.log("Subtraction of two given Matrices is: ");
console.log(matrixSubtraction(matrix1, matrix2));
console.log("\n");
console.log("Multiplication of two given Matrices is: ");
console.log(matrixMultiplication(matrix1, matrix2));
console.log("\n");
OutputAddition of two given Matrices is :
2 4 6
8 10 22
2 4 6
Subtraction of two given Matrices is :
0 0 0
0 0 -10
0 0 0
Multiplication of two given Matrices is :
12 18 44
30 45 110
12 18 44
Time Complexity:
The time complexity of the input() function is O(N^2) because it has to traverse the entire input matrix/vector of size NxN.
The time complexity of the display() function is also O(N^2) because it has to print all the elements of the matrix/vector.
The time complexity of the operator overloading functions for addition, subtraction, and multiplication of two matrices is O(N^3) because for each element in the output matrix, we need to calculate the sum/difference/product of N elements from the input matrices.
Therefore, the overall time complexity of the program is O(N^3) for each operator overload.
Auxiliary Space: O(N^2) because we need to store two matrices of size NxN in memory, which takes up O(N^2) space.
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