# 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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## 1 Answer

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.

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Thank you. Yeah, I just wanted to make sure that these are diagonal as well as I need to prove that they are zero divisors. –  alexcoco Sep 25 '12 at 15:21
@alexcoco No problem. Glad I could help clarify this. –  M Turgeon Sep 25 '12 at 15:23