Versal deformations of invariant subspaces
We describe a miniversal deformation of invariant subspaces (with regard to a fixed endomorphism) by means of a technique which can be applied to obtain explicitly miniversal deformations in a general orbit space. In addition, we present an application to the problem of classifying invariant subspac...
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| Vydáno v: | Linear algebra and its applications Ročník 332; s. 569 - 582 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Inc
01.08.2001
Elsevier |
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| ISSN: | 0024-3795, 1873-1856 |
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| Abstract | We describe a miniversal deformation of invariant subspaces (with regard to a fixed endomorphism) by means of a technique which can be applied to obtain explicitly miniversal deformations in a general orbit space. In addition, we present an application to the problem of classifying invariant subspaces. |
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| AbstractList | We describe a miniversal deformation of invariant subspaces (with regard to a fixed endomorphism) by means of a technique which can be applied to obtain explicitly miniversal deformations in a general orbit space. In addition, we present an application to the problem of classifying invariant subspaces.
Peer Reviewed We describe a miniversal deformation of invariant subspaces (with regard to a fixed endomorphism) by means of a technique which can be applied to obtain explicitly miniversal deformations in a general orbit space. In addition, we present an application to the problem of classifying invariant subspaces. |
| Author | Puerta, Ferran Ferrer, Josep |
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| Cites_doi | 10.1137/S0895479895284634 10.1016/0024-3795(95)00742-3 10.1090/S0002-9947-1982-0675077-2 10.1016/0001-8708(83)90044-0 10.1137/S0895479896310184 10.1016/0167-6911(85)90064-7 |
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| Contributor | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
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| References | Edelman, Elmroth, Kågström (BIBBIB2) 1997; 18 Arnold (BIBBIB1) 1971; 26 Shayman (BIBBIB7) 1982; 274 Humphreys (BIBBIB6) 1975 A. Tannenbaum, Invariance and System Theory Algebraic and Geometric Aspects, Lecture Notes in Mathematics, vol. 845, Springer, Berlin Tchon (BIBBIB9) 1985; 5 Edelman, Elmroth, Kågström (BIBBIB3) 1999; 20 Friedland (BIBBIB5) 1983; 50 Ferrer, Garcı́a, Puerta (BIBBIB4) 1997; 253 Edelman (10.1016/S0024-3795(01)00305-6_BIBBIB2) 1997; 18 Shayman (10.1016/S0024-3795(01)00305-6_BIBBIB7) 1982; 274 Humphreys (10.1016/S0024-3795(01)00305-6_BIBBIB6) 1975 Edelman (10.1016/S0024-3795(01)00305-6_BIBBIB3) 1999; 20 Friedland (10.1016/S0024-3795(01)00305-6_BIBBIB5) 1983; 50 Arnold (10.1016/S0024-3795(01)00305-6_BIBBIB1) 1971; 26 Ferrer (10.1016/S0024-3795(01)00305-6_BIBBIB4) 1997; 253 10.1016/S0024-3795(01)00305-6_BIBBIB8 Tchon (10.1016/S0024-3795(01)00305-6_BIBBIB9) 1985; 5 |
| References_xml | – volume: 5 start-page: 397 year: 1985 end-page: 401 ident: BIBBIB9 article-title: Bifurcation diagrams for feedback families of linear system publication-title: Systems Control Lett. – volume: 253 start-page: 175 year: 1997 end-page: 198 ident: BIBBIB4 article-title: Brunovsky local form of a holomorphic family of pairs of matrices publication-title: Linear Algebra Appl. – year: 1975 ident: BIBBIB6 publication-title: Linear Algebraic Groups – volume: 26 year: 1971 ident: BIBBIB1 article-title: On matrices depending on parameters publication-title: Uspekhi Mat. Nauk – volume: 50 start-page: 189 year: 1983 end-page: 265 ident: BIBBIB5 article-title: Simultaneous similarity of matrices publication-title: Adv. Math. – reference: A. Tannenbaum, Invariance and System Theory Algebraic and Geometric Aspects, Lecture Notes in Mathematics, vol. 845, Springer, Berlin – volume: 18 start-page: 653 year: 1997 end-page: 692 ident: BIBBIB2 article-title: A geometric approach to perturbation theory of matrices and matrix pencils. Part I. Versal deformations publication-title: SIAM J. Matrix Anal. Appl. – volume: 20 start-page: 667 year: 1999 end-page: 699 ident: BIBBIB3 article-title: A geometric approach to perturbation theory of matrices and matrix pencils. Part II. Stratification-enhanced staircase algorithm publication-title: SIAM J. Matrix Anal. Appl. – volume: 274 start-page: 721 year: 1982 end-page: 747 ident: BIBBIB7 article-title: On the variety of invariant subspaces of a finite-dimensional linear operator publication-title: Trans. Amer. Math. Soc. – volume: 18 start-page: 653 issue: 3 year: 1997 ident: 10.1016/S0024-3795(01)00305-6_BIBBIB2 article-title: A geometric approach to perturbation theory of matrices and matrix pencils. Part I. Versal deformations publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479895284634 – ident: 10.1016/S0024-3795(01)00305-6_BIBBIB8 – volume: 253 start-page: 175 year: 1997 ident: 10.1016/S0024-3795(01)00305-6_BIBBIB4 article-title: Brunovsky local form of a holomorphic family of pairs of matrices publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(95)00742-3 – volume: 274 start-page: 721 issue: 2 year: 1982 ident: 10.1016/S0024-3795(01)00305-6_BIBBIB7 article-title: On the variety of invariant subspaces of a finite-dimensional linear operator publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-1982-0675077-2 – volume: 50 start-page: 189 year: 1983 ident: 10.1016/S0024-3795(01)00305-6_BIBBIB5 article-title: Simultaneous similarity of matrices publication-title: Adv. Math. doi: 10.1016/0001-8708(83)90044-0 – volume: 20 start-page: 667 issue: 3 year: 1999 ident: 10.1016/S0024-3795(01)00305-6_BIBBIB3 article-title: A geometric approach to perturbation theory of matrices and matrix pencils. Part II. Stratification-enhanced staircase algorithm publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479896310184 – year: 1975 ident: 10.1016/S0024-3795(01)00305-6_BIBBIB6 – volume: 26 year: 1971 ident: 10.1016/S0024-3795(01)00305-6_BIBBIB1 article-title: On matrices depending on parameters publication-title: Uspekhi Mat. Nauk – volume: 5 start-page: 397 year: 1985 ident: 10.1016/S0024-3795(01)00305-6_BIBBIB9 article-title: Bifurcation diagrams for feedback families of linear system publication-title: Systems Control Lett. doi: 10.1016/0167-6911(85)90064-7 |
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| SubjectTerms | 15 Linear and multilinear algebra; matrix theory Algebras, Linear Classificació AMS invariant subspaces Matrices Matriu S, Teoria Multilinear algebra Àlgebra lineal Àlgebra multilineal |
| Title | Versal deformations of invariant subspaces |
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