The change of the Jordan structure of a mtrix under small perturbations
A.S. Markus,E.È. Parilis +1 more
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In this paper, a complete description including multiplicity is given for the Jordan structure of a matrix which is a small perturbation of a known Jordan structure, and the problem solved here was solved independently and the other solution has been published in English.About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-10-01 and is currently open access. It has received 43 citations till now.read more
Citations
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Similarity of block diagonal and block triangular matrices
TL;DR: It is shown that if a block triangular matrix is similar to its block diagonal part, then the similarity matrix can be chosen of the block triangular form and an analogous statement is proved for equivalent matrices.
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On a homeomorphism between orbit spaces of linear systems and matrix polynomials
S. Marcaida,Ion Zaballa +1 more
TL;DR: In this article, the authors considered the variation of the finite and left Wiener-Hopf structures under small perturbations of matrix polynomials with fixed degree for their determinants.
Safety Neighbourhoods for the Kronecker Canonical Form
TL;DR: In this paper, the authors give safety neighbourhoods for the necessary conditions in the change of the Kronecker canonical form of a matrix pencil under small perturbations, and show that these conditions can be achieved under some conditions.
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Jordan structures of upper equivalent matrices
TL;DR: In this article, the Jordan structures of strictly lower triangular completions of matrices over an algebraically closed field are studied and a sufficient condition for the existence of a completion which preserves the spectrum of the original matrix and has prescribed Jordan structure is given.
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Similarity and block similarity
TL;DR: Some equivalent characterizations of the block similarity of matrix pairs, with an application to a characterization of the similarity of two square matrices are presented.
References
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Calkin Algebras and Algebras of Operators on Banach SPates
TL;DR: In this paper, a treatment of the classical Riesz-Schauder theory is presented, which takes advantage of the most recent developments in functional analysis. But this treatment is restricted to the case of bounded linear operators on a Hilbert space.
Journal ArticleDOI
Equivalence, linearization, and decomposition of holomorphic operator functions
TL;DR: In this paper, it was shown that given a holomorphic function A on a bounded domain Ω into a space of bounded linear operators between two Banach spaces, it is possible to extend the operators A(λ) by an identity operator IZ in such a way that the extended operator function A(·) ⊕ IZ is equivalent on Ω to a linear function of λ, T − λI.