Notation: Indicate Non-Diagonal Entries Matrix

Question

What is the standard (or a widely used) way of indicating the non-diagonal elements of a matrix? I'm looking for something like this.

For matrix A: $$ A_{i,j \in i\neq j} $$ or perhaps this: $$ A_{i,j : i\neq j} $$

I am looking for a succinct way to write the equation: $$A_{i,j \in i\neq j} = \frac{1-a}{k}$$

Answer 1

Definitely a case for using words IMHO. For one thing, $$A_{i,j \in i\neq j}$$ gives the impression that it is some sort of modification of the $A_{i,j}$, whereas it is in fact a selection of the $A_{i,j}$. I would simply use one of the following, whichever fits better with the rest of the context:

• if $i\ne j$ then $A_{i,j} = \frac{1-a}{k}$

• $A_{i,j} = \frac{1-a}{k}$ whenever $i\ne j$

Answer 2

What about $\forall$ with $:$ ?

$$A_{i,j}=\frac{{1-a}}{{k}}\qquad\forall\ i,j \in (...) \ : i\neq j $$