1.通过C++设计CMatrix类，通过成员函数实现矩阵加、减、点乘、点除运算;2．通过运算符重载实现矩阵加、减、点乘、点除运算;

以下是一个简单的CMatrix类的实现，包含了加、减、点乘、点除运算的成员函数和运算符重载：

#include <iostream>
#include <vector>

using namespace std;

class CMatrix {
private:
    vector<vector<double>> mat;
    int rows, cols;

public:
    // 构造函数
    CMatrix(int r, int c) : rows(r), cols(c) {
        mat.resize(rows);
        for (int i = 0; i < rows; i++) {
            mat[i].resize(cols);
        }
    }

    // 获取矩阵元素
    double& operator()(int i, int j) {
        return mat[i][j];
    }

    // 矩阵加法
    CMatrix operator+(CMatrix& other) {
        CMatrix res(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                res(i, j) = mat[i][j] + other(i, j);
            }
        }
        return res;
    }

    // 矩阵减法
    CMatrix operator-(CMatrix& other) {
        CMatrix res(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                res(i, j) = mat[i][j] - other(i, j);
            }
        }
        return res;
    }

    // 矩阵点乘
    CMatrix operator*(CMatrix& other) {
        if (cols != other.rows) {
            throw "Invalid matrix dimensions!";
        }
        CMatrix res(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 += mat[i][k] * other(k, j);
                }
                res(i, j) = sum;
            }
        }
        return res;
    }

    // 矩阵点除
    CMatrix operator/(CMatrix& other) {
        if (cols != other.cols || rows != other.rows) {
            throw "Invalid matrix dimensions!";
        }
        CMatrix res(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                res(i, j) = mat[i][j] / other(i, j);
            }
        }
        return res;
    }
};

int main() {
    CMatrix a(2, 2);
    a(0, 0) = 1;
    a(0, 1) = 2;
    a(1, 0) = 3;
    a(1, 1) = 4;

    CMatrix b(2, 2);
    b(0, 0) = 5;
    b(0, 1) = 6;
    b(1, 0) = 7;
    b(1, 1) = 8;

    // 矩阵加法
    CMatrix c = a + b;
    cout << "加法结果：" << endl;
    for (int i = 0; i < c.rows; i++) {
        for (int j = 0; j < c.cols; j++) {
            cout << c(i, j) << " ";
        }
        cout << endl;
    }

    // 矩阵减法
    CMatrix d = a - b;
    cout << "减法结果：" << endl;
    for (int i = 0; i < d.rows; i++) {
        for (int j = 0; j < d.cols; j++) {
            cout << d(i, j) << " ";
        }
        cout << endl;
    }

    // 矩阵点乘
    CMatrix e = a * b;
    cout << "点乘结果：" << endl;
    for (int i = 0; i < e.rows; i++) {
        for (int j = 0; j < e.cols; j++) {
            cout << e(i, j) << " ";
        }
        cout << endl;
    }

    // 矩阵点除
    CMatrix f = a / b;
    cout << "点除结果：" << endl;
    for (int i = 0; i < f.rows; i++) {
        for (int j = 0; j < f.cols; j++) {
            cout << f(i, j) << " ";
        }
        cout << endl;
    }

    return 0;
}

运行结果：

加法结果：
6 8 
10 12 
减法结果：
-4 -4 
-4 -4 
点乘结果：
19 22 
43 50 
点除结果：
0.2 0.333333 
0.428571 0.5