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
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Coalescing Eigenvalues and Crossing Eigencurves of 1-Parameter Matrix Flows
TL;DR: The often misquoted and misapplied results by Hund and von Neumann and by Wigner for eigencurve crossings from the late 1920s are clarified and extended to general non-normal or non-hermitean 1-parameter matrix flows, leading to many new and open problems.
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The change of similarity invariants under row perturbations
TL;DR: In this article, the problem of the possible similarity classes of all the matrices obtained by small perturbations on some rows of a given complex square matrix is considered and necessary conditions on these similarity classes are provided.
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Cyclic dimensions, kernel multiplicities, and Gohberg-Kaashoek numbers
Vladimir Matsaev,Vadim Olshevsky +1 more
TL;DR: In this article, cyclic dimensions and kernel multiplicities are introduced for a square matrix and the connection between these characteristics and Gohberg-Kaashoek numbers is studied, and simple geometric proofs are given for the change of the Jordan structure of a given matrix under small perturbation.
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The change of similarity invariants under row perturbations: Generic cases☆
TL;DR: In this article, the problem of characterizing the possible invariant factors or Weyr characteristic of all the matrices that can be obtained from a specified one by perturbing some of its rows is considered.
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The change of feedback invariants under column perturbations: particular cases
TL;DR: In this article, the authors studied the variation of the feedback invariants of a complex rectangular n × (n + m) matrix when they make small additive perturbations to the elements of the last m columns.
References
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Book
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.
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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.