C++矩阵类的加减乘除运算的实现

矩阵类的加减乘除运算可以通过重载运算符来实现。以下是一个矩阵类的定义及其运算符重载实现示例：

#include <iostream>
#include <vector>

using namespace std;

class Matrix {
public:
    Matrix(int rows, int cols) : rows(rows), cols(cols) {
        data.resize(rows);
        for (int i = 0; i < rows; i++) {
            data[i].resize(cols);
        }
    }

    int getRows() const {
        return rows;
    }

    int getCols() const {
        return cols;
    }

    double& operator()(int i, int j) {
        return data[i][j];
    }

    const double& operator()(int i, int j) const {
        return data[i][j];
    }

    Matrix operator+(const Matrix& other) const {
        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result(i, j) = (*this)(i, j) + other(i, j);
            }
        }
        return result;
    }

    Matrix operator-(const Matrix& other) const {
        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result(i, j) = (*this)(i, j) - other(i, j);
            }
        }
        return result;
    }

    Matrix operator*(const Matrix& other) const {
        Matrix result(rows, other.cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < other.cols; j++) {
                double sum = 0;
                for (int k = 0; k < cols; k++) {
                    sum += (*this)(i, k) * other(k, j);
                }
                result(i, j) = sum;
            }
        }
        return result;
    }

    Matrix operator/(const Matrix& other) const {
        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result(i, j) = (*this)(i, j) / other(i, j);
            }
        }
        return result;
    }

private:
    int rows, cols;
    vector<vector<double>> data;
};

int main() {
    Matrix m1(2, 3);
    m1(0, 0) = 1;
    m1(0, 1) = 2;
    m1(0, 2) = 3;
    m1(1, 0) = 4;
    m1(1, 1) = 5;
    m1(1, 2) = 6;

    Matrix m2(3, 2);
    m2(0, 0) = 7;
    m2(0, 1) = 8;
    m2(1, 0) = 9;
    m2(1, 1) = 10;
    m2(2, 0) = 11;
    m2(2, 1) = 12;

    Matrix m3 = m1 * m2;

    for (int i = 0; i < m3.getRows(); i++) {
        for (int j = 0; j < m3.getCols(); j++) {
            cout << m3(i, j) << " ";
        }
        cout << endl;
    }

    return 0;
}

在这个示例中，矩阵类的构造函数接受行数和列数，并动态分配内存来存储矩阵数据。运算符重载实现中，加、减、乘、除分别对应了 `operator+`、`operator-`、`operator*`、`operator/`。`operator()` 用于访问矩阵元素。在 main 函数中，首先创建了两个矩阵 m1 和 m2，然后计算它们的乘积，并输出结果。