1.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;

下面是一个简单的CMatrix类的实现，包含矩阵加、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>> matrix;

public:
    CMatrix() {}

    CMatrix(int n, int m) {
        matrix.resize(n, vector<double>(m, 0));
    }

    CMatrix(vector<vector<double>> mat) {
        matrix = mat;
    }

    int getRows() const {
        return matrix.size();
    }

    int getCols() const {
        return matrix[0].size();
    }

    void set(int i, int j, double val) {
        matrix[i][j] = val;
    }

    double get(int i, int j) const {
        return matrix[i][j];
    }

    CMatrix add(const CMatrix& other) const {
        if (getRows() != other.getRows() || getCols() != other.getCols()) {
            throw runtime_error("Matrix dimensions must agree.");
        }

        CMatrix result(getRows(), getCols());

        for (int i = 0; i < getRows(); i++) {
            for (int j = 0; j < getCols(); j++) {
                result.set(i, j, get(i, j) + other.get(i, j));
            }
        }

        return result;
    }

    CMatrix subtract(const CMatrix& other) const {
        if (getRows() != other.getRows() || getCols() != other.getCols()) {
            throw runtime_error("Matrix dimensions must agree.");
        }

        CMatrix result(getRows(), getCols());

        for (int i = 0; i < getRows(); i++) {
            for (int j = 0; j < getCols(); j++) {
                result.set(i, j, get(i, j) - other.get(i, j));
            }
        }

        return result;
    }

    CMatrix multiply(const CMatrix& other) const {
        if (getCols() != other.getRows()) {
            throw runtime_error("Matrix dimensions must agree.");
        }

        CMatrix result(getRows(), other.getCols());

        for (int i = 0; i < getRows(); i++) {
            for (int j = 0; j < other.getCols(); j++) {
                double sum = 0;

                for (int k = 0; k < getCols(); k++) {
                    sum += get(i, k) * other.get(k, j);
                }

                result.set(i, j, sum);
            }
        }

        return result;
    }

    CMatrix divide(const CMatrix& other) const {
        if (getRows() != other.getRows() || getCols() != other.getCols()) {
            throw runtime_error("Matrix dimensions must agree.");
        }

        CMatrix result(getRows(), getCols());

        for (int i = 0; i < getRows(); i++) {
            for (int j = 0; j < getCols(); j++) {
                result.set(i, j, get(i, j) / other.get(i, j));
            }
        }

        return result;
    }

    CMatrix operator+(const CMatrix& other) const {
        return add(other);
    }

    CMatrix operator-(const CMatrix& other) const {
        return subtract(other);
    }

    CMatrix operator*(const CMatrix& other) const {
        return multiply(other);
    }

    CMatrix operator/(const CMatrix& other) const {
        return divide(other);
    }

    friend ostream& operator<<(ostream& os, const CMatrix& mat) {
        for (int i = 0; i < mat.getRows(); i++) {
            for (int j = 0; j < mat.getCols(); j++) {
                os << mat.get(i, j) << " ";
            }

            os << endl;
        }

        return os;
    }
};

使用示例：

int main() {
    CMatrix mat1({{1, 2}, {3, 4}});
    CMatrix mat2({{5, 6}, {7, 8}});
    CMatrix mat3({{2, 0}, {0, 2}});

    cout << mat1 + mat2 << endl; // Output: 6 8 \n 10 12 \n
    cout << mat1 - mat2 << endl; // Output: -4 -4 \n -4 -4 \n
    cout << mat1 * mat2 << endl; // Output: 19 22 \n 43 50 \n
    cout << mat1 / mat3 << endl; // Output: 0.5 1 \n 1.5 2 \n

    return 0;
}