As far as I understand, a diagonal matrix is one whose non-zero elements are on the main diagonal. Am I correct in assuming that the diagonal can contain zeros as well? ie:
$$ \begin{bmatrix} 0&0 \\ 0&1 \\ \end{bmatrix} $$ and $$ \begin{bmatrix} 1&0 \\ 0&0 \\ \end{bmatrix} $$
are also diagonal matrices.