| Full text | |
| Author(s): |
Futorny, Vyacheslav
;
Horn, Roger A.
;
Sergeichuk, Vladimir V.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Linear Algebra and its Applications; v. 519, p. 278-295, APR 15 2017. |
| Web of Science Citations: | 3 |
| Abstract | |
W. Specht (1940) proved that two n x n complex matrices A and B are unitarily similar if and only if trace w(A, A{*}) = trace w(B, B{*}) for every word w(x, y) in two noncommuting variables. We extend his criterion and its generalizations by N.A. Wiegmann (1961) and N. Jing (2015) to an arbitrary system A consisting of complex or real inner product spaces and linear mappings among them. We represent such a system by the directed graph Q(A), whose vertices are inner product spaces and arrows are linear mappings. Denote by (Q) over tilde (A) the directed graph obtained by enlarging to Q(A) the adjoint linear mappings. We prove that a system A is transformed by isometries of its spaces to a system 13 if and only if the traces of all closed directed walks in Q(A) and Q(13) coincide. (C) 2017 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 14/09310-5 - Algebraic structures and their representations |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 15/05864-9 - Classification problems in linear algebra and system theory |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |