Is there something like reverse of relation

Question

Is there some term in math for something like reverse of relation?

So we have relation in matrix form for example:

  A B C
A 0 1 1
B 1 0 0
C 1 0 0 

And I want to mathematically express exactly opposite :

  A B C
A 1 0 0
B 0 1 1
C 0 1 1

Is there some notation for this?

Answer 1

Yes. If you think of a relation as a subset $R$ of some $A\times A$, then the complementary relation is just $(A\times A)\setminus R$. If you use relation-oriented notation, then you would just write it with a slash through the relation, like $S\not\subset T$.

Answer 2

You may call it the complement of the original relation.

Note that two elements are related originally if and only if they are not related with the new relation.

If you want the inverse relation you have to find the transpose of the original matrix.