Partially Specified Matrices and Operators: Classification, Completion, Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1995
|
| Schriftenreihe: | Operator Theory Advances and Applications
79 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is devoted to a new direction in linear algebra and operator theory that deals with the invariants of partially specified matrices and operators, and with the spectral analysis of their completions. The theory developed centers around two major problems concerning matrices of which part of the entries are given and the others are unspecified. The first is a classification problem and aims at a simplification of the given part with the help of admissible similarities. The results here may be seen as a far reaching generalization of the Jordan canonical form. The second problem is called the eigenvalue completion problem and asks to describe all possible eigenvalues and their multiplicities of the matrices which one obtains by filling in the unspecified entries. Both problems are also considered in an infinite dimensional operator framework. A large part of the book deals with applications to matrix theory and analysis, namely to stabilization problems in mathematical system theory, to problems of Wiener-Hopf factorization and interpolation for matrix polynomials and rational matrix functions, to the Kronecker structure theory of linear pencils, and to non everywhere defined operators. The eigenvalue completion problem has a natural associated inverse, which appears as a restriction problem. The analysis of these two problems is often simpler when a solution of the corresponding classification problem is available |
| Beschreibung: | 1 Online-Ressource (368p) |
| ISBN: | 9783034891004 9783034899062 |
| DOI: | 10.1007/978-3-0348-9100-4 |
Internformat
MARC
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| 245 | 1 | 0 | |a Partially Specified Matrices and Operators: Classification, Completion, Applications |c by Israel Gohberg, Marinus A. Kaashoek, Frederik Schagen |
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| 490 | 0 | |a Operator Theory Advances and Applications |v 79 | |
| 500 | |a This book is devoted to a new direction in linear algebra and operator theory that deals with the invariants of partially specified matrices and operators, and with the spectral analysis of their completions. The theory developed centers around two major problems concerning matrices of which part of the entries are given and the others are unspecified. The first is a classification problem and aims at a simplification of the given part with the help of admissible similarities. The results here may be seen as a far reaching generalization of the Jordan canonical form. The second problem is called the eigenvalue completion problem and asks to describe all possible eigenvalues and their multiplicities of the matrices which one obtains by filling in the unspecified entries. Both problems are also considered in an infinite dimensional operator framework. A large part of the book deals with applications to matrix theory and analysis, namely to stabilization problems in mathematical system theory, to problems of Wiener-Hopf factorization and interpolation for matrix polynomials and rational matrix functions, to the Kronecker structure theory of linear pencils, and to non everywhere defined operators. The eigenvalue completion problem has a natural associated inverse, which appears as a restriction problem. The analysis of these two problems is often simpler when a solution of the corresponding classification problem is available | ||
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Datensatz im Suchindex
| _version_ | 1804153096516927488 |
|---|---|
| any_adam_object | |
| author | Gohberg, Yiśrāʿēl Z. 1928-2009 |
| author_GND | (DE-588)118915878 (DE-588)122738497 (DE-588)115064729 |
| author_facet | Gohberg, Yiśrāʿēl Z. 1928-2009 |
| author_role | aut |
| author_sort | Gohberg, Yiśrāʿēl Z. 1928-2009 |
| author_variant | y z g yz yzg |
| building | Verbundindex |
| bvnumber | BV042422296 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879623178 (DE-599)BVBBV042422296 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-9100-4 |
| format | Electronic eBook |
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| id | DE-604.BV042422296 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034891004 9783034899062 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857713 |
| oclc_num | 879623178 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (368p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Birkhäuser Basel |
| record_format | marc |
| series2 | Operator Theory Advances and Applications |
| spelling | Gohberg, Yiśrāʿēl Z. 1928-2009 Verfasser (DE-588)118915878 aut Partially Specified Matrices and Operators: Classification, Completion, Applications by Israel Gohberg, Marinus A. Kaashoek, Frederik Schagen Basel Birkhäuser Basel 1995 1 Online-Ressource (368p) txt rdacontent c rdamedia cr rdacarrier Operator Theory Advances and Applications 79 This book is devoted to a new direction in linear algebra and operator theory that deals with the invariants of partially specified matrices and operators, and with the spectral analysis of their completions. The theory developed centers around two major problems concerning matrices of which part of the entries are given and the others are unspecified. The first is a classification problem and aims at a simplification of the given part with the help of admissible similarities. The results here may be seen as a far reaching generalization of the Jordan canonical form. The second problem is called the eigenvalue completion problem and asks to describe all possible eigenvalues and their multiplicities of the matrices which one obtains by filling in the unspecified entries. Both problems are also considered in an infinite dimensional operator framework. A large part of the book deals with applications to matrix theory and analysis, namely to stabilization problems in mathematical system theory, to problems of Wiener-Hopf factorization and interpolation for matrix polynomials and rational matrix functions, to the Kronecker structure theory of linear pencils, and to non everywhere defined operators. The eigenvalue completion problem has a natural associated inverse, which appears as a restriction problem. The analysis of these two problems is often simpler when a solution of the corresponding classification problem is available Mathematics Matrix theory Global analysis (Mathematics) Systems theory Mathematical optimization Analysis Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Matrizentheorie (DE-588)4128970-5 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Eigenwert (DE-588)4151200-5 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Vervollständigung Mathematik (DE-588)4309936-1 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Operator (DE-588)4130529-2 s Vervollständigung Mathematik (DE-588)4309936-1 s Spektraltheorie (DE-588)4116561-5 s 1\p DE-604 Matrix Mathematik (DE-588)4037968-1 s 2\p DE-604 Matrizentheorie (DE-588)4128970-5 s 3\p DE-604 Eigenwert (DE-588)4151200-5 s 4\p DE-604 Lineare Algebra (DE-588)4035811-2 s 5\p DE-604 Matrizenrechnung (DE-588)4126963-9 s 6\p DE-604 Kaashoek, Marinus A. 1937- Sonstige (DE-588)122738497 oth Schagen, Frederik van 1944- Sonstige (DE-588)115064729 oth https://doi.org/10.1007/978-3-0348-9100-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gohberg, Yiśrāʿēl Z. 1928-2009 Partially Specified Matrices and Operators: Classification, Completion, Applications Mathematics Matrix theory Global analysis (Mathematics) Systems theory Mathematical optimization Analysis Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Matrizentheorie (DE-588)4128970-5 gnd Matrizenrechnung (DE-588)4126963-9 gnd Eigenwert (DE-588)4151200-5 gnd Matrix Mathematik (DE-588)4037968-1 gnd Spektraltheorie (DE-588)4116561-5 gnd Vervollständigung Mathematik (DE-588)4309936-1 gnd Lineare Algebra (DE-588)4035811-2 gnd Operator (DE-588)4130529-2 gnd |
| subject_GND | (DE-588)4128970-5 (DE-588)4126963-9 (DE-588)4151200-5 (DE-588)4037968-1 (DE-588)4116561-5 (DE-588)4309936-1 (DE-588)4035811-2 (DE-588)4130529-2 |
| title | Partially Specified Matrices and Operators: Classification, Completion, Applications |
| title_auth | Partially Specified Matrices and Operators: Classification, Completion, Applications |
| title_exact_search | Partially Specified Matrices and Operators: Classification, Completion, Applications |
| title_full | Partially Specified Matrices and Operators: Classification, Completion, Applications by Israel Gohberg, Marinus A. Kaashoek, Frederik Schagen |
| title_fullStr | Partially Specified Matrices and Operators: Classification, Completion, Applications by Israel Gohberg, Marinus A. Kaashoek, Frederik Schagen |
| title_full_unstemmed | Partially Specified Matrices and Operators: Classification, Completion, Applications by Israel Gohberg, Marinus A. Kaashoek, Frederik Schagen |
| title_short | Partially Specified Matrices and Operators: Classification, Completion, Applications |
| title_sort | partially specified matrices and operators classification completion applications |
| topic | Mathematics Matrix theory Global analysis (Mathematics) Systems theory Mathematical optimization Analysis Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Matrizentheorie (DE-588)4128970-5 gnd Matrizenrechnung (DE-588)4126963-9 gnd Eigenwert (DE-588)4151200-5 gnd Matrix Mathematik (DE-588)4037968-1 gnd Spektraltheorie (DE-588)4116561-5 gnd Vervollständigung Mathematik (DE-588)4309936-1 gnd Lineare Algebra (DE-588)4035811-2 gnd Operator (DE-588)4130529-2 gnd |
| topic_facet | Mathematics Matrix theory Global analysis (Mathematics) Systems theory Mathematical optimization Analysis Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Matrizentheorie Matrizenrechnung Eigenwert Matrix Mathematik Spektraltheorie Vervollständigung Mathematik Lineare Algebra Operator |
| url | https://doi.org/10.1007/978-3-0348-9100-4 |
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