写一段C++代码使用 Vector 类和定义派生类 Matrix实现矩阵的基本算术运算

下面是使用Vector类和定义派生类Matrix实现矩阵的基本算术运算的C++代码：

#include <iostream>
#include <vector>

using namespace std;

class Vector {
public:
    int size;
    vector<double> data;

    Vector(int n) {
        size = n;
        data.resize(n);
    }

    Vector operator+(const Vector& A) {
        Vector res(size);
        for (int i = 0; i < size; i++)
            res.data[i] = data[i] + A.data[i];
        return res;
    }

    Vector operator-(const Vector& A) {
        Vector res(size);
        for (int i = 0; i < size; i++)
            res.data[i] = data[i] - A.data[i];
        return res;
    }

    Vector operator*(const double& a) {
        Vector res(size);
        for (int i = 0; i < size; i++)
            res.data[i] = data[i] * a;
        return res;
    }

    double operator*(const Vector& A) {
        double res = 0;
        for (int i = 0; i < size; i++)
            res += data[i] * A.data[i];
        return res;
    }
};

class Matrix : public Vector {
public:
    int rows, cols;

    Matrix(int m, int n) : Vector(m * n) {
        rows = m;
        cols = n;
    }

    Vector operator[](int i) {
        Vector res(cols);
        for (int j = 0; j < cols; j++)
            res.data[j] = data[i * cols + j];
        return res;
    }

    Matrix operator+(const Matrix& A) {
        Matrix res(rows, cols);
        for (int i = 0; i < size; i++)
            res.data[i] = data[i] + A.data[i];
        return res;
    }

    Matrix operator-(const Matrix& A) {
        Matrix res(rows, cols);
        for (int i = 0; i < size; i++)
            res.data[i] = data[i] - A.data[i];
        return res;
    }

    Matrix operator*(const double& a) {
        Matrix res(rows, cols);
        for (int i = 0; i < size; i++)
            res.data[i] = data[i] * a;
        return res;
    }

    Matrix operator*(const Matrix& A) {
        Matrix res(rows, A.cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < A.cols; j++) {
                Vector row = (*this)[i];
                Vector col = A.getColumn(j);
                res[i * res.cols + j] = row * col;
            }
        }
        return res;
    }

    Vector getColumn(int j) {
        Vector res(rows);
        for (int i = 0; i < rows; i++)
            res.data[i] = data[i * cols + j];
        return res;
    }
};

int main() {
    Matrix A(3, 2);
    A.data = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0};
    Matrix B(2, 3);
    B.data = {7.0, 8.0, 9.0, 10.0, 11.0, 12.0};
    Matrix C = A * B;
    for (int i = 0; i < C.rows; i++) {
        for (int j = 0; j < C.cols; j++) {
            cout << C[i][j] << " ";
        }
        cout << endl;
    }
    return 0;
}

这段代码中，Vector类表示一维向量，包含加、减、数乘和点乘等基本运算符重载；Matrix类是Vector类的派生类，表示二维矩阵，重载了加、减、数乘、矩阵乘等运算符，并且可以通过下标索引获取矩阵的行向量和列向量。在main函数中，我们定义了两个矩阵A和B，并计算它们的乘积C，最后输出结果。