Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599596 | Linear Algebra and its Applications | 2014 | 17 Pages |
Abstract
Two mÃn pencils A+λB and Aâ²+λBâ² over F=R or C are said to be topologically equivalent if the pairs of linear mappings A,B:FnâFm and Aâ²,Bâ²:FnâFm coincide up to homeomorphisms of the spaces Fn and Fm. 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 Dâ² such that the linear operators D,Dâ²:FrâFr coincide up to a homeomorphism of Fr.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Vyacheslav Futorny, Tetiana Rybalkina, Vladimir V. Sergeichuk,