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Dmytryshyn, Andrii

Open this publication in new window or tab >>Geometry of Matrix Polynomial Spaces### Dmytryshyn, Andrii

### Johansson, Stefan

### Kågström, Bo

### Van Dooren, Paul

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_some",{id:"formSmash:j_idt191:0:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_0_j_idt195_otherAuthors",{id:"formSmash:j_idt191:0:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_0_j_idt195_otherAuthors",multiple:true}); 2019 (English)In: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

##### Keywords

Matrix polynomials, Stratifications, Matrix pencils, Fiedler linearization, Canonical structure information, Orbit, Bundle
##### National Category

Computational Mathematics Computer and Information Sciences
##### Identifiers

urn:nbn:se:umu:diva-163512 (URN)10.1007/s10208-019-09423-1 (DOI)
#####

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##### Funder

eSSENCE - An eScience CollaborationSwedish Research Council, E0485301
Available from: 2019-09-24 Created: 2019-09-24 Last updated: 2019-10-03

Umeå University, Faculty of Science and Technology, Department of Computing Science. School of Science and Technology, Örebro University, Örebro, Sweden.

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Department of Mathematical Engineering, Université catholique de Louvain, Louvain-la-Neuve, Belgium.

We study how small perturbations of general matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy (stratification) graphs of matrix polynomials' orbits and bundles. To solve this problem, we construct the stratification graphs for the first companion Fiedler linearization of matrix polynomials. Recall that the first companion Fiedler linearization as well as all the Fiedler linearizations is matrix pencils with particular block structures. Moreover, we show that the stratification graphs do not depend on the choice of Fiedler linearization which means that all the spaces of the matrix polynomial Fiedler linearizations have the same geometry (topology). This geometry coincides with the geometry of the space of matrix polynomials. The novel results are illustrated by examples using the software tool StratiGraph extended with associated new functionality.

Open this publication in new window or tab >>Miniversal deformations of pairs of symmetric matrices under congruence### Dmytryshyn, Andrii

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_some",{id:"formSmash:j_idt191:1:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_otherAuthors",{id:"formSmash:j_idt191:1:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_otherAuthors",multiple:true}); 2019 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 568, p. 84-105Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2019
##### Keywords

Symmetric matrix pair, Symmetric matrix pencil, Congruence canonical form, Perturbation, Versal formation, Codimension
##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:umu:diva-157936 (URN)10.1016/j.laa.2018.05.034 (DOI)000462111400005 ()
#####

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Available from: 2019-04-18 Created: 2019-04-18 Last updated: 2019-04-18Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

For each pair of complex symmetric matrices (A, B) we provide a normal form with a minimal number of independent parameters, to which all pairs of complex symmetric matrices ((A) over tilde (B) over tilde), close to (A, B) can be reduced by congruence transformation that smoothly depends on the entries of (A ) over tilde and (B) over tilde. Such a normal form is called a miniversal deformation of (A, B) under congruence. A number of independent parameters in the miniversal deformation of a symmetric matrix pencil is equal to the codimension of the congruence orbit of this symmetric matrix pencil and is computed too. We also provide an upper bound on the distance from (A, B) to its miniversal deformation.

Open this publication in new window or tab >>Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade### Dmytryshyn, Andrii

### Dopico, Froilán

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_some",{id:"formSmash:j_idt191:2:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_otherAuthors",{id:"formSmash:j_idt191:2:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 536, p. 1-18Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2018
##### Keywords

Complete eigenstructure, Genericity, Matrix polynomials, Skew-symmetry, Normal rank, Orbits, Pencils
##### National Category

Algebra and Logic
##### Research subject

business data processing
##### Identifiers

urn:nbn:se:umu:diva-139925 (URN)10.1016/j.laa.2017.09.006 (DOI)000414814500001 ()
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##### Funder

Swedish Research Council, E0485301
Available from: 2017-09-26 Created: 2017-09-26 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Universidad Carlos III de Madrid.

We show that the set of m×m complex skew-symmetric matrix polynomials of odd grade *d*, i.e., of degree at most *d*, and (normal) rank at most 2*r* is the closure of the single set of matrix polynomials with the certain, explicitly described, complete eigenstructure. This complete eigenstructure corresponds to the most generic m×m complex skew-symmetric matrix polynomials of odd grade *d* and rank at most 2*r*. In particular, this result includes the case of skew-symmetric matrix pencils (d=1).

Open this publication in new window or tab >>Canonical structure transitions of system pencils### Dmytryshyn, Andrii

### Johansson, Stefan

### Kågström, Bo

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_some",{id:"formSmash:j_idt191:3:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_otherAuthors",{id:"formSmash:j_idt191:3:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_otherAuthors",multiple:true}); 2017 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 38, no 4, p. 1249-1267Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Society for Industrial and Applied Mathematics, 2017
##### National Category

Mathematics Computer and Information Sciences
##### Research subject

business data processing
##### Identifiers

urn:nbn:se:umu:diva-139924 (URN)10.1137/16M1097857 (DOI)000418665600009 ()
#####

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##### Funder

Swedish Research Council, E0485301Swedish Research Council, eSSENCE
Available from: 2017-09-26 Created: 2017-09-26 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).

Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).

We investigate the changes of the canonical structure information under small perturbations for a system pencil associated with a (generalized) linear time-invariant state-space system. The equivalence class of the pencil is taken with respect to feedback-injection equivalence transformations. The results allow us to track possible changes of important linear system characteristics under small perturbations.

Open this publication in new window or tab >>Generalization of Roth's solvability criteria to systems of matrix equations### Dmytryshyn, Andrii

### Futorny, Vyacheslav

### Klymchuk, Tetiana

### Sergeichuk, Vladimir V.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_some",{id:"formSmash:j_idt191:4:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_otherAuthors",{id:"formSmash:j_idt191:4:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_otherAuthors",multiple:true}); 2017 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 527, p. 294-302Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Systems of matrix equations, Sylvester equations, Roth's criteria
##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:umu:diva-136303 (URN)10.1016/j.laa.2017.04.011 (DOI)000402344000014 ()
#####

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##### Funder

Swedish Research Council, E0485301
Available from: 2017-06-29 Created: 2017-06-29 Last updated: 2019-04-18Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

W.E. Roth (1952) proved that the matrix equation AX - XB = C has a solution if and only if the matrices [Graphics] and [Graphics] are similar. A. Dmytryshyn and B. Kagstrom (2015) extended Roth's criterion to systems of matrix equations A(i)X(i')M(i) - (NiXi"Bi)-B-sigma i = Ci (i = 1,..., s) with unknown matrices X1,, X-t, in which every X-sigma is X, X-T, or X*. We extend their criterion to systems of complex matrix equations that include the complex conjugation of unknown matrices. We also prove an analogous criterion for systems of quaternion matrix equations. (C) 2017 Elsevier Inc. All rights reserved.

Open this publication in new window or tab >>Generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree### Dmytryshyn, Andrii

### Dopico, Froilán M.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_some",{id:"formSmash:j_idt191:5:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_otherAuthors",{id:"formSmash:j_idt191:5:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_otherAuthors",multiple:true}); 2017 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 535, p. 213-230Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2017
##### Keywords

Complete eigenstructure, Genericity, Matrix polynomials, Normal rank, Orbits
##### National Category

Computer and Information Sciences Mathematics
##### Identifiers

urn:nbn:se:umu:diva-139923 (URN)10.1016/j.laa.2017.09.007 (DOI)000413058000012 ()
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##### Funder

Swedish Research Council, E0485301Swedish Research Council, eSSENCEStiftelsen Längmanska kulturfonden, BA17-1175
Available from: 2017-09-26 Created: 2017-09-26 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Universidad Carlos III de Madrid.

The set POL_{d,}_{r}^{m}^{×n} of *m*×*n* complex matrix polynomials of grade *d* and (normal) rank at most *r* in a complex (*d*+1)*mn* dimensional space is studied. For *r*=1,...,min{*m*,*n*}−1, we show that POL_{d,}_{r}^{m}^{×n} is the union of the closures of the *rd*+1 sets of matrix polynomials with rank *r*, degree exactly *d*, and explicitly described complete eigenstructures. In addition, for the full-rank rectangular polynomials, i.e. *r*=min{*m*,*n*} and *m*≠*n*, we show that POL_{d,}_{r}^{m}^{×n} coincides with the closure of a single set of the polynomials with rank *r*, degree exactly *d*, and the described complete eigenstructure. These complete eigenstructures correspond to generic *m*×*n* matrix polynomials of grade *d* and rank at most *r*.

Open this publication in new window or tab >>Structure preserving stratification of skew-symmetric matrix polynomials### Dmytryshyn, Andrii

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_some",{id:"formSmash:j_idt191:6:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_otherAuthors",{id:"formSmash:j_idt191:6:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_otherAuthors",multiple:true}); 2017 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 532, p. 266-286Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2017
##### Keywords

Skew-symmetric matrix polynomials, Matrix polynomials, Stratifications, Skew-symmetric matrix pencils, Orbit, Bundle
##### National Category

Algebra and Logic Computational Mathematics
##### Research subject

Computer Science; business data processing
##### Identifiers

urn:nbn:se:umu:diva-139922 (URN)10.1016/j.laa.2017.06.044 (DOI)000411297500017 ()
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##### Funder

Swedish Research Council, E0485301Swedish Research Council, eSSENCE
Available from: 2017-09-26 Created: 2017-09-26 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

We study how elementary divisors and minimal indices of a skew-symmetric matrix polynomial of odd degree may change under small perturbations of the matrix coefficients. We investigate these changes qualitatively by constructing the stratifications (closure hierarchy graphs) of orbits and bundles for skew-symmetric linearizations. We also derive the necessary and sufficient conditions for the existence of a skew-symmetric matrix polynomial with prescribed degree, elementary divisors, and minimal indices.

Open this publication in new window or tab >>Classification of pairs of linear mappings between two vector spaces and between their quotient space and subspace### Dmytryshyn, Andrii

### Fonseca, Carlos

### Rybalkina, Tetiana

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_some",{id:"formSmash:j_idt191:7:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_otherAuthors",{id:"formSmash:j_idt191:7:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_otherAuthors",multiple:true}); 2016 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 509, p. 228-246Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Canonical forms; Pairs of linear mappings; Matrix pencils
##### National Category

Computer Sciences
##### Identifiers

urn:nbn:se:umu:diva-139978 (URN)10.1016/j.laa.2016.07.016 (DOI)000385338000011 ()
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Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

We classify pairs of linear mappings (U -> V, U/U' -> V') in which U, V are finite dimensional vector spaces over a field IF, and U', are their subspaces. (C) 2016 Elsevier Inc. All rights reserved.

Open this publication in new window or tab >>Generic matrix polynomials with fixed rank and fixed degree### Dmytryshyn, Andrii

### Dopico, Froilán M.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_some",{id:"formSmash:j_idt191:8:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_otherAuthors",{id:"formSmash:j_idt191:8:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_otherAuthors",multiple:true}); 2016 (English)Report (Other academic)
##### Place, publisher, year, edition, pages

Umeå: Umeå Universitet, 2016. p. 18
##### Series

Report / UMINF, ISSN 0348-0542 ; 16/19
##### Keywords

complete eigenstructure, genericity, matrix polynomials, normal rank, orbits
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-129341 (URN)
#####

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##### Funder

Swedish Research Council, E0485301eSSENCE - An eScience Collaboration
Available from: 2016-12-22 Created: 2016-12-22 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Departamento de Matemáticas, Universidad Carlos III de Madrid.

Open this publication in new window or tab >>Miniversal deformations of pairs of skew-symmetric matrices under congruence### Dmytryshyn, Andrii

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_some",{id:"formSmash:j_idt191:9:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_otherAuthors",{id:"formSmash:j_idt191:9:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_otherAuthors",multiple:true}); 2016 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 506, p. 506-534Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Skew-symmetric matrix pair, Skew-symmetric matrix pencil, Congruence canonical form, Congruence, Perturbation, Versal deformation
##### National Category

Mathematical Analysis
##### Identifiers

urn:nbn:se:umu:diva-127581 (URN)10.1016/j.laa.2016.06.015 (DOI)000381954300024 ()
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Available from: 2016-12-13 Created: 2016-11-16 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Computing Science.

Miniversal deformations for pairs of skew-symmetric matrices under congruence are constructed. To be precise, for each such a pair (A, B) we provide a normal form with a minimal number of independent parameters to which all pairs of skew-symmetric matrices ((A) over tilde (,) (B) over tilde), close to (A, B) can be reduced by congruence transformation which smoothly depends on the entries of the matrices in the pair ((A) over tilde (,) (B) over tilde). An upper bound on the distance from such a miniversal deformation to (A, B) is derived too. We also present an example of using miniversal deformations for analyzing changes in the canonical structure information (i.e. eigenvalues and minimal indices) of skew-symmetric matrix pairs under perturbations.