The change of the Jordan structure of a mtrix under small perturbations
A.S. Markus,E.È. Parilis +1 more
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TLDR
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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Matrices with prescribed rows and invariant factors
TL;DR: In this article, the existence of an n × n matrix over an arbitrary field when its invariant polynomials and either some rows or columns are prescribed is solved in terms of invariant factor inequalities and of majorization inequalities involving controllability indices and the degrees of the invariants.
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A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification-Enhanced Staircase Algorithm
TL;DR: It is proposed that knowledge of the closure relations, i.e., the stratification, of the orbits and bundles of the various forms may be applied in the staircase algorithm.
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Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence
TL;DR: In this article, the Hasse diagrams G2 and G3 were constructed for the closure ordering on the sets of congruence classes of 2 × 2 and 3 × 3 complex matrices.
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Perturbation of linear control systems
TL;DR: In this article, the variation of controllability indices and the Jordan structure of a pair of matrices under small perturbations was studied, and it was shown that the Jordan structures of the two matrices A and B can be obtained from the controllable indices.
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Triangularizing matrix polynomials
TL;DR: In this article, it was shown that any matrix polynomial in an algebraically closed field can be reduced to triangular form, preserving the degree and the finite and infinite elementary divisors.
References
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Remark on Weyl's Note “Inequalities Between the Two Kinds of Eigenvalues of a Linear Transformation”
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Inequalities for certain Classes of Convex Functions
TL;DR: In this article, the same idea was used to derive a whole series of results on convex functions, in particular Hardy-Littlewood-Polya and Polya will emerge as special cases.
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Unsolved problems in matrix and operator theory, I. Partial multiplicities and additive perturbations
TL;DR: In this article, the authors pose a problem concerning the behavior of the sizes of the blocks in a Jordan matrix under small additive perturbations and present a solution to the problem.