Is this definition of diagonal matrix correct?

Question

I need to know if the following definition:

Let $A:=\|a_{i,j}\|_{\substack{i=1,...,m \\ j=1,...,m}}$ be a square matrix. $A$ is diagonal matrix if $$i\neq j \implies a_{ij}=0, \quad\forall i,j \in \{1,...,m\}$$

is correct?

Thanks in advance!

Answer 1

Yes, it's correct. By the way, $\|\cdot\|$ is more or less an obsolete notation for matrices. The modern notation is to use a pair of round or square brackets, i.e. $(a_{i,j})_{\substack{i=1,...,m \\ j=1,...,m}}$ or $[a_{i,j}]_{\substack{i=1,...,m \\ j=1,...,m}}$, and $\|\cdot\|$ is now usually used to denote a vector or matrix norm.