Pointer to portions of array. Overloading [] operator to access portions of array

Following the question in Pointer to portions of array, a structure that does operations with portions of an array was proposed.

I would like to request one further question within this issue.

I would like to create a structure for blockMatrices using std::vector and would require to change the implementation of the structure for getting a 3x3 matrix out of a 4x4 matrix.

The current test case is:

#include <vector>
#include <array>
#include <iostream>

// define matrix 4x4
typedef std::array<double, 16> matrix4;

// define matrix 3x3
typedef std::array<double, 9>  matrix3;

// get 3x3 matrix out of a 4x4 matrix
struct subMat
{
    matrix4& matrix_;

    const double& operator[](size_t index) const
    {
        static size_t mapping[] = {0, 1, 2, 4, 5, 6, 8, 9, 10};
        return matrix_[mapping[index]];
    }    
    subMat (matrix4& A): matrix_(A){}
};

template <typename T>
double sum_of_elements(const T& arr)
{
    double res = 0;
    for (int i=0;i < 9; ++i)
    {
        res += arr[i];
    } 
    return res;
}

int main(int argCount, char *args[])
{
    std::vector<matrix4> myBlockMatrix(5);

    for (int i=0; i < myBlockMatrix.size(); i++)
    {
        for (int j = 0; j<myBlockMatrix[0].size(); j++)
        {
            myBlockMatrix[i][j] = i*j;
        }
    }

    for (int i = 0; i<myBlockMatrix.size(); i++)
    {
        std::cout << sum_of_elements(subMat(myBlockMatrix[i])) << std::endl; // this works
    }

    subBlockMatrix subBlock (myBlockMatrix);
    for (int i = 0; i<myBlockMatrix.size(); i++)
    {
        std::cout << sum_of_elements(subBlock[i])) << std::endl; 
    } 

    return 0;
}

For overloading the [] operator, I have:

struct subBlockMatrix : std::vector<matrix4>
{
    std::vector<matrix4>& blockMatrix_;

    const matrix4& operator[](std::size_t index) const
    {   
        static size_t mapping[] = {0, 1, 2, 4, 5, 6, 8, 9, 10};
        return blockMatrix_[mapping[index]];
    } 
    subBlockMatrix(std::vector<matrix4>& A) : blockMatrix_(A) {}
};

But this does not work... I am having difficulty understanding how to make it work and would really appreciate the help!

Best Regards