Generic canonical form of pairs of matrices with zeros
Representation Theory
2007-10-08 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0710.1273,
title = {Generic canonical form of pairs of matrices with zeros},
author = {Tatyana N. Gaiduk and Vladimir V. Sergeichuk},
journal= {arXiv preprint arXiv:0710.1273},
year = {2007}
}
Comments
13 pages