Structural Stability of Matrix Pencils and Matrix Pairs Under Contragredient Equivalence

A complex matrix pencil A− ⋋ B is called structurally stable if there exists its neighborhood in which all pencils are strictly equivalent to this pencil. We describe all complex matrix pencils that are structurally stable. It is shown that there are no pairs ( M,N ) of m × n and n × m complex matri...

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Bibliographic Details
Published in:Ukrainian mathematical journal Vol. 71; no. 5; pp. 808 - 811
Main Authors: García-Planas, M. I., Klymchuk, T.
Format: Journal Article Publication
Language:English
Published: New York Springer US 01.10.2019
Springer
Subjects:
15 Linear and multilinear algebra; matrix theory
Algebra
Analysis
Applications of Mathematics
Brief Communications
Classificació AMS
Contragredient equivalence
Differential equations, Linear
Equacions diferencials lineals
Geometry
Matemàtiques i estadística
Mathematics
Mathematics and Statistics
Matrices
Matrius (Matemàtica)
Matrix pair
Statistics
Structural stability
Àrees temàtiques de la UPC
ISSN:0041-5995, 1573-9376
Online Access:Get full text
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Summary:A complex matrix pencil A− ⋋ B is called structurally stable if there exists its neighborhood in which all pencils are strictly equivalent to this pencil. We describe all complex matrix pencils that are structurally stable. It is shown that there are no pairs ( M,N ) of m × n and n × m complex matrices ( m, n ≥ 1) that are structurally stable under the contragredient equivalence ( S − 1 MR,R − 1 NS ) in which S and R are nondegenerate.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-019-01676-x