Author
E.È. Parilis
Bio: E.È. Parilis is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 41 citations.
Papers
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TL;DR: 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.
43 citations
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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.
112 citations
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.
Abstract: Computing the Jordan form of a matrix or the Kronecker structure of a pencil is a well-known ill-posed problem We propose that knowledge of the closure relations, ie, the stratification, of the orbits and bundles of the various forms may be applied in the staircase algorithm Here we discuss and complete the mathematical theory of these relationships and show how they may be applied to the staircase algorithm This paper is a continuation of our Part I paper on versal deformations, but it may also be read independently
93 citations
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.
32 citations
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.
31 citations
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.
26 citations