TITLE: Diagonal Matrices with Zero on Diagonal
QUESTION [5 upvotes]: 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.

REPLY [4 votes]: Indeed, you are right, there may be zero elements on the diagonal. But your definition of diagonal matrix is slightly ambiguous. A clearer definition (in my opinion) is that all off-diagonal entries are zero.