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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: $$A_{i,j \in i\neq j} = \frac{1-a}{k}$$

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    How about just saying what you mean? "$A_{i,j}$ where $i\ne j$". Or are you not allowed to use words? – 2017-01-19
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    i would prefer a more succinct form as it is part of a larger equation but that could work – 2017-01-19
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    In that case perhaps you should post the larger equation, otherwise it's hard for people to know what you really want. – 2017-01-19
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    Thanks, see edited question. – 2017-01-19

2 Answers 2

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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 $i\ne j$

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What about $\forall$ with $:$ ?

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