transitivity of a relation, through matrix.

Question

Is there a formula/algorithm to check whether any relation is transitive, using its matrix?

I seem to have found a formula $\sum_{i=1}^{n} \sum_{j=1}^{n} \sum_{k=1}^{n}$[ M^T_kj*(M^T_ki-1)]=0

You should provide relevant details(elaborate your findings; perhaps add a quick description of how a matrix can be used to represent a relation-useful refresher for users who might not be particularly inclined to look it up), or risk the question being downvoted. Having said that, are you vaguely referring to finding the square of the boolean matrix and comparing to it to the original? — Akay, Feb 27 '17 at 18:54
No, not that, this is quite different. It doesn't involve multiplication, just writing down the transpose of the matrix, and comparing some elements. (Which I think is similar to finding the square) I think I should provide details. — Swaroop Joshi, Feb 27 '17 at 18:56
Possible duplicate of How to check whether a relation is transitive from the matrix representation? — Akay, Feb 27 '17 at 18:58
You've got to be more descriptive. For example, what is implied if the above summation is zero? I assume M is the boolean matrix representing the relation in question; but you'd do well to mention that. — Akay, Feb 27 '17 at 19:18

score 1 · Answer 1 · edited Apr 13 '17 at 12:21

1

Given such a logical matrix $A$, the square of the matrix $A^2$ shouldn't have non-zero in any place where $A$ has a zero.

edited Apr 13 '17 at 12:21

Community

answered Feb 27 '17 at 18:53

Tangent Bundle

1 Answers1