# Diagonal Matrices with Zero on Diagonal

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.

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