I have been shown the following Hadamard delta function to be represented as a 2D array:
$$\delta_H (u,v) = \begin{cases} 1 & u=u_0\,\,\mathrm{and}\,\,v=v_0 \tag{2}\\ 0 &\mathrm{otherwise}. \end{cases}$$
In my understanding, u represents the x-axis and v the y-axis and $(u_0, v_0) = (3,3)$ (central), so unless I am reading this incorrectly, in my head if we had a 6 x 6 matrix, it would look like:
$$\begin{matrix} 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0\\ \end{matrix}$$
This does not look right for me, as the matrix would always look the same independetly of the matrices being used. In the following link the matrices produced via MATLAB code, do not look like this, but I don't understand why their is different.
How should the delta function be represented like "matrixwise".
This is based on :
Hadamard single-pixel imaging versus Fourier single-pixel imaging (2017) by Z. Zhang