| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Sao Paulo, Dept Math, BR-05508 Sao Paulo - Brazil
[2] Inst Math, Kiev - Ukraine
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Linear Algebra and its Applications; v. 450, p. 121-137, JUN 1 2014. |
| Web of Science Citations: | 2 |
| Abstract | |
By Kronecker's theorem, each matrix pencil A + lambda B over a field F is strictly equivalent to its regularizing decomposition; i.e., a direct sum (I-r + lambda D) circle plus (M-1 + lambda N-1)(mt + ANt), where D is an r x r nonsingular matrix and each M-i + lambda N-i, is of the form I-k + lambda(k) (0), J(k) (0) + lambda I-k, L-k + lambda Rk, or L-k(T) + lambda R-k(T), in which L-k and R-k are obtained from I-k by deleting its last or, respectively, first row and J(k) (0) is a singular Jordan block. We give a method for constructing a regularizing decomposition of an m x n matrix pencil A + lambda B, which is formulated in terms of the linear mappings A, B : F-n -> F-m. Two m x n pencils A + lambda B and A' + lambda B' over F = R or C are said to be topologically equivalent if the pairs of linear mappings A, B : F-n -> F-m and A', B' : F-n -> F-m coincide up to homeomorphisms of the spaces F-n and F-m. We prove that two pencils are topologically equivalent if and only if their regularizing decompositions coincide up to permutation of summands and replacement of D by a nonsingular matrix D' such that the linear operators D,D' : F-r -> F-r coincide up to a homeomorphism of F-r. (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 |