Combinatorial analysis of generic matrix pencils

Authors:
Satoru Iwata;Ryo Shimizu
Affiliations:
University of Tokyo, Tokyo, Japan;University of Tokyo, Tokyo, Japan
Venue:
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Year:
2005

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Abstract

This paper investigates the Kronecker canonical form of matrix pencils under the genericity assumption that the set of nonzero entries is algebraically independent. We provide a combinatorial characterization of the sums of the row/column indices supported by efficient bipartite matching algorithms. We also give a simple alternative proof for a theorem of Poljak on the generic ranks of matrix powers.