Diagonal Matrix is Symmetric

Theorem
Let $D$ be a diagonal matrix.

Then $D$ is symmetric.

Proof
By definition of diagonal matrix:
 * $\forall j, k: j \ne k \implies a_{jk} = 0 = a_{kj}$

So by definition of transpose of $D$:
 * $D = D^\intercal$

where $D^\intercal$ denotes the transpose.

Hence the result, by definition of symmetric matrix.