Confused about diagonal matix notation Reading a book of physics I found the following definition of diagonal matrix:
$$A_{ij}= A_{ii}\delta_{ij}$$
I understand a diagonal matrix has only diagonal elements nonzero, but is the previous notation correct? 
I'm somehow confused because if we choose $A_{ij}$ with $i\neq j $ (f.e $A_{12}$) then we need to use $A_{11}$ from the right side, which seems a bit forced.

It's correct, if $i=j$, $A_{ij}=A_{ii}\delta_{ij}=A_{ii}\cdot 1 = A_{ii}$
if $i\ne j$, $A_{ij}=A_{ii}\delta_{ij}=A_{ii}\cdot 0 = 0$
