| Full text | |
| Author(s): |
Dmytryshyn, Andrii
[1, 2]
;
Futorny, Vyacheslav
[3]
;
Kagstrom, Bo
[1, 2]
;
Klimenko, Lena
[4]
;
Sergeichuk, Vladimir V.
[5]
Total Authors: 5
|
| Affiliation: | [1] Umea Univ, Dept Comp Sci, S-90187 Umea - Sweden
[2] Umea Univ, HPC2N, S-90187 Umea - Sweden
[3] Univ Sao Paulo, Dept Math, BR-05508 Sao Paulo - Brazil
[4] Natl Tech Univ Ukraine, Kyiv Polytech Inst, Kiev - Ukraine
[5] Ukrainian Acad Sci, Inst Math, Kiev - Ukraine
Total Affiliations: 5
|
| Document type: | Journal article |
| Source: | Linear Algebra and its Applications; v. 469, p. 305-334, MAR 15 2015. |
| Web of Science Citations: | 5 |
| Abstract | |
We construct the Hasse diagrams G(2) and G(3) for the closure ordering on the sets of congruence classes of 2 x 2 and 3 x 3 complex matrices. In other words, we construct two directed graphs whose vertices are 2 x 2 or, respectively, 3 x 3 canonical matrices under congruence, and there is a directed path from A to B if and only if A can be transformed by an arbitrarily small perturbation to a matrix that is congruent to B. A bundle of matrices under congruence is defined as a set of square matrices A for which the pencils A)AT belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of 2 x 2 or 3 x 3 matrices have the same properties with respect to perturbations. We construct the Hasse diagrams G(2)(B) and G(3)(B) for the closure ordering on the sets of congruence bundles of 2 x 2 and, respectively, 3 x 3 matrices. We find the isometry groups of 2 x 2 and 3 x 3 congruence canonical matrices. (C) 2014 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 10/50347-9 - Algebras, representations e applications |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 12/18139-2 - Methods of representation theory in linear algebra |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |