Determining if logical matrix represents a partial order

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If we represent a relation using a logical matrix (so that if (a,b) is present in the relation then the element at row a and column b in the matrix is a 1), is there any way to determine that this matrix represents a partial order using matrix operations?

For example, if we have the relation {(1,1),(2,2),(3,3),(1,2)} represented by this matrix:

[tex]
\left( \begin{array}{ccc}
1 & 1 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \end{array} \right)
[/tex]

Is there some way, using matrix operations, to determine if this represents a partial order?
 
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Answers and Replies

  • #2
Actually, yes. This is a convenient way. For instance, see Mathematics of Fuzziness -- Basic Issues by Xuzhu Wang, Da Raun and Etienne E. Kerre.
 

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