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Kågström, Bo
##### Publications (10 of 10) Show all publications
Dmytryshyn, A., Johansson, S. & Kågström, B. (2017). Canonical structure transitions of system pencils. SIAM Journal on Matrix Analysis and Applications, 38(4), 1249-1267
Open this publication in new window or tab >>Canonical structure transitions of system pencils
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]

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.

##### Keywords
linear system, generalized state-space system, system pencil, matrix pencil, orbit, bundle, perturbation, versal deformation, stratification
##### National Category
Computer Sciences Mathematical Analysis
##### Identifiers
urn:nbn:se:oru:diva-74889 (URN)10.1137/16M1097857 (DOI)000418665600009 ()2-s2.0-85022337450 (Scopus ID)
##### Funder
Swedish Research Council, E0485301eSSENCE - An eScience Collaboration Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved
Dmytryshyn, A., Johansson, S. & Kågström, B. (2015). Canonical structure transitions of system pencils. Umeå: Umeå universitet
Open this publication in new window or tab >>Canonical structure transitions of system pencils
##### Abstract [en]

We investigate the changes under small perturbations of the canonical structure information for a system pencil (A B C D) − s (E 0 0 0), det(E) ≠ 0, associated with a (generalized) linear time-invariant state-space system. The equivalence class of the pencil is taken with respect to feedback-injection equivalence transformation. The results allow to track possible changes under small perturbations of important linear system characteristics.

##### Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2015. p. 26
##### Series
UMINF, ISSN 0348-0542 ; 5
##### Keywords
Linear system, descriptor system, state-space system, system pencil, matrix pencil, orbit, bundle, perturbation, versal deformation, stratification
##### National Category
Mathematics Computer and Information Sciences Electrical Engineering, Electronic Engineering, Information Engineering Civil Engineering
##### Identifiers
urn:nbn:se:oru:diva-74888 (URN)
##### Funder
eSSENCE - An eScience CollaborationSwedish Research Council, E048530 Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-08-06Bibliographically approved
Dmytryshyn, A., Futorny, V., Kågström, B., Klimenko, L. & Sergeichuk, V. (2015). Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence. Linear Algebra and its Applications, 469, 305-334
Open this publication in new window or tab >>Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence
2015 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 469, p. 305-334Article in journal (Refereed) Published
##### Abstract [en]

We construct the Hasse diagrams G2 and G3 for the closure ordering on the sets of congruence classes of 2 × 2 and 3 × 3 complex matrices. In other words, we construct two directed graphs whose vertices are 2 × 2 or, respectively, 3 × 3 canonical matrices under congruence, and there is a directed path from A to B if and only if A can be transformed by an arbitrarily small perturbation to a matrix that is congruent to B. A bundle of matrices under congruence is defined as a set of square matrices A for which the pencils A + λAT belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of 2 × 2 or 3 × 3 matrices have the same properties with respect to perturbations. We construct the Hasse diagrams G2 B and G3 B for the closure ordering on the sets of congruence bundles of 2 × 2 and, respectively, 3 × 3 matrices. We find the isometry groups of 2 × 2 and 3 × 3 congruence canonical matrices.

Elsevier, 2015
##### Keywords
Bundle, Closure graph, Congruence canonical form, Congruence class, Perturbation
##### National Category
Mathematical Analysis
##### Identifiers
urn:nbn:se:oru:diva-74885 (URN)10.1016/j.laa.2014.11.004 (DOI)000348883600014 ()2-s2.0-84919935890 (Scopus ID)
##### Funder
eSSENCE - An eScience CollaborationSwedish Research Council, A0581501 Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved
Dmytryshyn, A. & Kågström, B. (2015). Coupled Sylvester-type Matrix Equations and Block Diagonalization. SIAM Journal on Matrix Analysis and Applications, 36(2), 580-593
Open this publication in new window or tab >>Coupled Sylvester-type Matrix Equations and Block Diagonalization
2015 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 36, no 2, p. 580-593Article in journal (Refereed) Published
##### Abstract [en]

We prove Roth-type theorems for systems of matrix equations including an arbitrary mix of Sylvester and $\star$-Sylvester equations, in which the transpose or conjugate transpose of the unknown matrices also appear. In full generality, we derive consistency conditions by proving that such a system has a solution if and only if the associated set of $2 \times 2$ block matrix representations of the equations are block diagonalizable by (linked) equivalence transformations. Various applications leading to several particular cases have already been investigated in the literature, some recently and some long ago. Solvability of these cases follow immediately from our general consistency theory. We also show how to apply our main result to systems of Stein-type matrix equations.

##### Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2015
##### Keywords
matrix equation, Sylvester equation, Stein equation, Roth's theorem, consistency, block diagonalization
##### National Category
Computer Sciences Mathematical Analysis
##### Identifiers
urn:nbn:se:oru:diva-74892 (URN)10.1137/151005907 (DOI)000357407800011 ()2-s2.0-84936772205 (Scopus ID)
Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved
Dmytryshyn, A., Johansson, S., Kågström, B. & Van Dooren, P. (2015). Geometry of spaces for matrix polynomial Fiedler linearizations. Umeå: Umeå universitet
Open this publication in new window or tab >>Geometry of spaces for matrix polynomial Fiedler linearizations
##### Abstract [en]

We study how small perturbations of matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy graphs (stratifications) of orbits and bundles of matrix polynomial Fiedler linearizations. We show that the stratifica-tion graphs do not depend on the choice of Fiedler linearization which means that all the spaces of the matrix polynomial Fiedler lineariza-tions have the same geometry (topology). The results are illustrated by examples using the software tool StratiGraph.

##### Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2015. p. 28
##### Series
UMINF, ISSN 0348-0542 ; 15/17
##### National Category
Mathematics Computer and Information Sciences
##### Identifiers
urn:nbn:se:oru:diva-74891 (URN)
##### Funder
Swedish Research Council, E0485301eSSENCE - An eScience Collaboration Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-08-06Bibliographically approved
Dmytryshyn, A. & Kågström, B. (2014). Orbit closure hierarchies of skew-symmetric matrix pencils. Umeå: Umeå universitet
Open this publication in new window or tab >>Orbit closure hierarchies of skew-symmetric matrix pencils
##### Abstract [en]

We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skew-symmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another skew-symmetric matrix pencil. This theory relies on our main theorem stating that a skew-symmetric matrix pencil A-λB can be approximated by pencils strictly equivalent to a skew-symmetric matrix pencil C-λD if and only if A-λB can be approximated by pencils congruent to C-λD.

##### Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2014. p. 18
##### Series
UMINF, ISSN 0348-0542 ; 14/02
##### Keywords
Skew-symmetric matrix pencil, stratification, canonical structure information, orbits
##### National Category
Computer Sciences Computational Mathematics
##### Identifiers
urn:nbn:se:oru:diva-74894 (URN)
Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-08-06Bibliographically approved
Dmytryshyn, A. & Kågström, B. (2014). Orbit closure hierarchies of skew-symmetric matrix pencils. SIAM Journal on Matrix Analysis and Applications, 35(4), 1429-1443
Open this publication in new window or tab >>Orbit closure hierarchies of skew-symmetric matrix pencils
2014 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 35, no 4, p. 1429-1443Article in journal (Refereed) Published
##### Abstract [en]

We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skew-symmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another skew-symmetric matrix pencil. The developed theory relies on our main theorem stating that a skew-symmetric matrix pencil A - lambda B can be approximated by pencils strictly equivalent to a skew-symmetric matrix pencil C - lambda D if and only if A - lambda B can be approximated by pencils congruent to C - lambda D.

##### Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2014
##### Keywords
skew-symmetric matrix pencil, stratification, canonical structure information, orbit, bundle
##### National Category
Computer Sciences
##### Identifiers
urn:nbn:se:oru:diva-74893 (URN)10.1137/140956841 (DOI)000346843200010 ()2-s2.0-84919931822 (Scopus ID)
##### Funder
eSSENCE - An eScience CollaborationSwedish Research Council, A0581501 Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved
Dmytryshyn, A., Kågström, B. & Sergeichuk, V. V. (2014). Symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations. The Electronic Journal of Linear Algebra, 27, 1-18
Open this publication in new window or tab >>Symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations
2014 (English)In: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 27, p. 1-18Article in journal (Refereed) Published
##### Abstract [en]

The set of all solutions to the homogeneous system of matrix equations (X-T A + AX, X-T B + BX) = (0, 0), where (A, B) is a pair of symmetric matrices of the same size, is characterized. In addition, the codimension of the orbit of (A, B) under congruence is calculated. This paper is a natural continuation of the article [A. Dmytryshyn, B. Kagstrom, and V. V. Sergeichuk. Skew-symmetric matrix pencils: Codimension counts and the solution of a pair of matrix equations. Linear Algebra Appl., 438:3375-3396, 2013.], where the corresponding problems for skew-symmetric matrix pencils are solved. The new results will be useful in the development of the stratification theory for orbits of symmetric matrix pencils.

##### Keywords
Pair of symmetric matrices, Matrix equations, Orbits, Codimension
##### National Category
Algebra and Logic
##### Identifiers
urn:nbn:se:oru:diva-74896 (URN)10.13001/1081-3810.1602 (DOI)000331236500001 ()2-s2.0-84894423199 (Scopus ID)
##### Funder
eSSENCE - An eScience CollaborationSwedish Research Council, A0581501 Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved
Dmytryshyn, A., Johansson, S. & Kågström, B. (2013). Codimension computations of congruence orbits of matrices, symmetric and skew-symmetric matrix pencils using Matlab. Umeå: Umeå Universitet
Open this publication in new window or tab >>Codimension computations of congruence orbits of matrices, symmetric and skew-symmetric matrix pencils using Matlab
##### Abstract [en]

Matlab functions to work with the canonical structures for congru-ence and *congruence of matrices, and for congruence of symmetricand skew-symmetric matrix pencils are presented. A user can providethe canonical structure objects or create (random) matrix examplesetups with a desired canonical information, and compute the codi-mensions of the corresponding orbits: if the structural information(the canonical form) of a matrix or a matrix pencil is known it isused for the codimension computations, otherwise they are computednumerically. Some auxiliary functions are provided too. All thesefunctions extend the Matrix Canonical Structure Toolbox.

##### Place, publisher, year, edition, pages
Umeå: Umeå Universitet, 2013. p. 41
##### Series
UMINF, ISSN 0348-0542 ; 13/18
##### Keywords
Congruence; *congruence; Symmetric matrix pencils; Skew-symmetric matrix pencils; Orbits; Codimension; MATLAB
##### National Category
Computer Sciences Computational Mathematics
##### Research subject
Numerical Analysis; Computer Science
##### Identifiers
urn:nbn:se:oru:diva-74890 (URN)
Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-08-06Bibliographically approved
Dmytryshyn, A., Kågström, B. & Sergeichuk, V. V. (2013). Skew-symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations. Linear Algebra and its Applications, 438(8), 3375-3396
Open this publication in new window or tab >>Skew-symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations
2013 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 438, no 8, p. 3375-3396Article in journal (Refereed) Published
##### Abstract [en]

The homogeneous system of matrix equations (X(T)A + AX, (XB)-B-T + BX) = (0, 0), where (A, B) is a pair of skew-symmetric matrices of the same size is considered: we establish the general solution and calculate the codimension of the orbit of (A, B) under congruence. These results will be useful in the development of the stratification theory for orbits of skew-symmetric matrix pencils.

Elsevier, 2013
##### Keywords
Pair of skew-symmetric matrices, Matrix equations, Orbits, Codimension
##### National Category
Algebra and Logic
##### Identifiers
urn:nbn:se:oru:diva-74895 (URN)10.1016/j.laa.2012.11.025 (DOI)000316521500015 ()2-s2.0-84875429601 (Scopus ID)
##### Funder
eSSENCE - An eScience CollaborationSwedish Research Council, A0581501 Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved

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