Computing the generic jordan canonical form

Incidence matrix and cover matrix of nested interval orders

“…Weyr's Theorem [30] says that the two nilpotent matrices Ò P and C P have the same Jordan invariants if and only if rank C (Ò k P ) = rank C (C k P ) for every k. So, it is interesting to test for which ℓ we have rank(Ò k P ) = rank(C k P ) for every k ≤ ℓ. We refer to [2,3,4,11,13,19,23,25,26,27,29] for some work on Jordan canonical forms determined by combinatorial patterns and refer to [12,22] for some work on ranks of matrix powers determined by combinatorial patterns. …”