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Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
University of Sao Paulo, Brazil .
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
Kiev Polytechnic Institute, Ukraine.
Vise andre og tillknytning
2015 (engelsk)Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 469, s. 305-334Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We construct the Hasse diagrams G2 and G3 for the closure ordering on the sets of congruence classes of 2 × 2 and 3 × 3 complex matrices. In other words, we construct two directed graphs whose vertices are 2 × 2 or, respectively, 3 × 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 + λAT belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of 2 × 2 or 3 × 3 matrices have the same properties with respect to perturbations. We construct the Hasse diagrams G2 B and G3 B for the closure ordering on the sets of congruence bundles of 2 × 2 and, respectively, 3 × 3 matrices. We find the isometry groups of 2 × 2 and 3 × 3 congruence canonical matrices.

sted, utgiver, år, opplag, sider
2015. Vol. 469, s. 305-334
Emneord [en]
Bundle, Closure graph, Congruence canonical form, Congruence class, Perturbation
HSV kategori
Forskningsprogram
matematik; administrativ databehandling
Identifikatorer
URN: urn:nbn:se:umu:diva-101053DOI: 10.1016/j.laa.2014.11.004ISI: 000348883600014Scopus ID: 2-s2.0-84919935890OAI: oai:DiVA.org:umu-101053DiVA, id: diva2:796288
Forskningsfinansiär
eSSENCE - An eScience CollaborationSwedish Research Council, A0581501Tilgjengelig fra: 2015-03-18 Laget: 2015-03-18 Sist oppdatert: 2018-06-07bibliografisk kontrollert

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Dmytryshyn, AndriiKågström, Bo

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