Generic canonical form of pairs of matrices with zeros

Details Generic canonical form of pairs of matrices with zeros Generic canonical form of pairs of matrices with zeros

2007-10-05

arxiv.org/abs/0710.1273v1

Linear Algebra Appl. 380 (2004) 241-251

Mathematics

Representation Theory

13 pages

Scientific paper

10.1016/j.laa.2003.10.011

We consider a family of pairs of m-by-p and m-by-q matrices, in which some entries are required to be zero and the others are arbitrary, with respect to transformations (A,B)--> (SAR,SBL) with nonsingular S, R, L. We prove that almost all of these pairs reduce to the same pair (C, D) from this family, except for pairs whose arbitrary entries are zeros of a certain polynomial. The polynomial and the pair (C D) are constructed by a combinatorial method based on properties of a certain graph.

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