Simultaneous Triangularization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2000
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A collection of matrices is said to be triangularizable if there is an invertible matrix S such that S1 AS is upper triangular for every A in the collection. This generalization of commutativity is the subject of many classical theorems due to Engel, Kolchin, Kaplansky, McCoy and others. The concept has been extended to collections of bounded linear operators on Banach spaces: such a collection is defined to be triangularizable if there is a maximal chain of subspaces of the Banach space, each of which is invariant under every member of the collection. Most of the classical results have been generalized to compact operators, and there are also recent theorems in the finite-dimensional case. This book is the first comprehensive treatment of triangularizability in both the finite and infinite-dimensional cases. It contains numerous very recent results and new proofs of many of the classical theorems. It provides a thorough background for research in both the linear-algebraic and operator-theoretic aspects of triangularizability and related areas. More generally, the book will be useful to anyone interested in matrices or operators, as many of the results are linked to other topics such as spectral mapping theorems, properties of spectral radii and traces, and the structure of semigroups and algebras of operators. It is essentially self-contained modulo solid courses in linear algebra (for the first half) and functional analysis (for the second half), and is therefore suitable as a text or reference for a graduate course |
| Beschreibung: | 1 Online-Ressource (XII, 319 p) |
| ISBN: | 9781461212003 9780387984667 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4612-1200-3 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042419780 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2000 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461212003 |c Online |9 978-1-4612-1200-3 | ||
| 020 | |a 9780387984667 |c Print |9 978-0-387-98466-7 | ||
| 024 | 7 | |a 10.1007/978-1-4612-1200-3 |2 doi | |
| 035 | |a (OCoLC)863675973 | ||
| 035 | |a (DE-599)BVBBV042419780 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 512.5 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Radjavi, Heydar |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Simultaneous Triangularization |c by Heydar Radjavi, Peter Rosenthal |
| 264 | 1 | |a New York, NY |b Springer New York |c 2000 | |
| 300 | |a 1 Online-Ressource (XII, 319 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Universitext |x 0172-5939 | |
| 500 | |a A collection of matrices is said to be triangularizable if there is an invertible matrix S such that S1 AS is upper triangular for every A in the collection. This generalization of commutativity is the subject of many classical theorems due to Engel, Kolchin, Kaplansky, McCoy and others. The concept has been extended to collections of bounded linear operators on Banach spaces: such a collection is defined to be triangularizable if there is a maximal chain of subspaces of the Banach space, each of which is invariant under every member of the collection. Most of the classical results have been generalized to compact operators, and there are also recent theorems in the finite-dimensional case. This book is the first comprehensive treatment of triangularizability in both the finite and infinite-dimensional cases. It contains numerous very recent results and new proofs of many of the classical theorems. It provides a thorough background for research in both the linear-algebraic and operator-theoretic aspects of triangularizability and related areas. More generally, the book will be useful to anyone interested in matrices or operators, as many of the results are linked to other topics such as spectral mapping theorems, properties of spectral radii and traces, and the structure of semigroups and algebras of operators. It is essentially self-contained modulo solid courses in linear algebra (for the first half) and functional analysis (for the second half), and is therefore suitable as a text or reference for a graduate course | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Matrix theory | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Linear and Multilinear Algebras, Matrix Theory | |
| 650 | 4 | |a Analysis | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Dreieckszerlegung |0 (DE-588)4324733-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Triangulation |0 (DE-588)4186017-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Matrizenalgebra |0 (DE-588)4139347-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Triangulation |0 (DE-588)4186017-2 |D s |
| 689 | 0 | 1 | |a Matrizenalgebra |0 (DE-588)4139347-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Dreieckszerlegung |0 (DE-588)4324733-7 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 700 | 1 | |a Rosenthal, Peter |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4612-1200-3 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027855197 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153090797993984 |
|---|---|
| any_adam_object | |
| author | Radjavi, Heydar |
| author_facet | Radjavi, Heydar |
| author_role | aut |
| author_sort | Radjavi, Heydar |
| author_variant | h r hr |
| building | Verbundindex |
| bvnumber | BV042419780 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863675973 (DE-599)BVBBV042419780 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1200-3 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03545nmm a2200565zc 4500</leader><controlfield tag="001">BV042419780</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2000 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461212003</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4612-1200-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387984667</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-387-98466-7</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4612-1200-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863675973</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042419780</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.5</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Radjavi, Heydar</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Simultaneous Triangularization</subfield><subfield code="c">by Heydar Radjavi, Peter Rosenthal</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">2000</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 319 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Universitext</subfield><subfield code="x">0172-5939</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">A collection of matrices is said to be triangularizable if there is an invertible matrix S such that S1 AS is upper triangular for every A in the collection. This generalization of commutativity is the subject of many classical theorems due to Engel, Kolchin, Kaplansky, McCoy and others. The concept has been extended to collections of bounded linear operators on Banach spaces: such a collection is defined to be triangularizable if there is a maximal chain of subspaces of the Banach space, each of which is invariant under every member of the collection. Most of the classical results have been generalized to compact operators, and there are also recent theorems in the finite-dimensional case. This book is the first comprehensive treatment of triangularizability in both the finite and infinite-dimensional cases. It contains numerous very recent results and new proofs of many of the classical theorems. It provides a thorough background for research in both the linear-algebraic and operator-theoretic aspects of triangularizability and related areas. More generally, the book will be useful to anyone interested in matrices or operators, as many of the results are linked to other topics such as spectral mapping theorems, properties of spectral radii and traces, and the structure of semigroups and algebras of operators. It is essentially self-contained modulo solid courses in linear algebra (for the first half) and functional analysis (for the second half), and is therefore suitable as a text or reference for a graduate course</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrix theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global analysis (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear and Multilinear Algebras, Matrix Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Dreieckszerlegung</subfield><subfield code="0">(DE-588)4324733-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Triangulation</subfield><subfield code="0">(DE-588)4186017-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Matrizenalgebra</subfield><subfield code="0">(DE-588)4139347-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Triangulation</subfield><subfield code="0">(DE-588)4186017-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Matrizenalgebra</subfield><subfield code="0">(DE-588)4139347-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Dreieckszerlegung</subfield><subfield code="0">(DE-588)4324733-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rosenthal, Peter</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4612-1200-3</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027855197</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042419780 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461212003 9780387984667 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855197 |
| oclc_num | 863675973 |
| 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 (XII, 319 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Universitext |
| spelling | Radjavi, Heydar Verfasser aut Simultaneous Triangularization by Heydar Radjavi, Peter Rosenthal New York, NY Springer New York 2000 1 Online-Ressource (XII, 319 p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 A collection of matrices is said to be triangularizable if there is an invertible matrix S such that S1 AS is upper triangular for every A in the collection. This generalization of commutativity is the subject of many classical theorems due to Engel, Kolchin, Kaplansky, McCoy and others. The concept has been extended to collections of bounded linear operators on Banach spaces: such a collection is defined to be triangularizable if there is a maximal chain of subspaces of the Banach space, each of which is invariant under every member of the collection. Most of the classical results have been generalized to compact operators, and there are also recent theorems in the finite-dimensional case. This book is the first comprehensive treatment of triangularizability in both the finite and infinite-dimensional cases. It contains numerous very recent results and new proofs of many of the classical theorems. It provides a thorough background for research in both the linear-algebraic and operator-theoretic aspects of triangularizability and related areas. More generally, the book will be useful to anyone interested in matrices or operators, as many of the results are linked to other topics such as spectral mapping theorems, properties of spectral radii and traces, and the structure of semigroups and algebras of operators. It is essentially self-contained modulo solid courses in linear algebra (for the first half) and functional analysis (for the second half), and is therefore suitable as a text or reference for a graduate course Mathematics Matrix theory Global analysis (Mathematics) Linear and Multilinear Algebras, Matrix Theory Analysis Mathematik Dreieckszerlegung (DE-588)4324733-7 gnd rswk-swf Triangulation (DE-588)4186017-2 gnd rswk-swf Matrizenalgebra (DE-588)4139347-8 gnd rswk-swf Triangulation (DE-588)4186017-2 s Matrizenalgebra (DE-588)4139347-8 s 1\p DE-604 Dreieckszerlegung (DE-588)4324733-7 s 2\p DE-604 Rosenthal, Peter Sonstige oth https://doi.org/10.1007/978-1-4612-1200-3 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 |
| spellingShingle | Radjavi, Heydar Simultaneous Triangularization Mathematics Matrix theory Global analysis (Mathematics) Linear and Multilinear Algebras, Matrix Theory Analysis Mathematik Dreieckszerlegung (DE-588)4324733-7 gnd Triangulation (DE-588)4186017-2 gnd Matrizenalgebra (DE-588)4139347-8 gnd |
| subject_GND | (DE-588)4324733-7 (DE-588)4186017-2 (DE-588)4139347-8 |
| title | Simultaneous Triangularization |
| title_auth | Simultaneous Triangularization |
| title_exact_search | Simultaneous Triangularization |
| title_full | Simultaneous Triangularization by Heydar Radjavi, Peter Rosenthal |
| title_fullStr | Simultaneous Triangularization by Heydar Radjavi, Peter Rosenthal |
| title_full_unstemmed | Simultaneous Triangularization by Heydar Radjavi, Peter Rosenthal |
| title_short | Simultaneous Triangularization |
| title_sort | simultaneous triangularization |
| topic | Mathematics Matrix theory Global analysis (Mathematics) Linear and Multilinear Algebras, Matrix Theory Analysis Mathematik Dreieckszerlegung (DE-588)4324733-7 gnd Triangulation (DE-588)4186017-2 gnd Matrizenalgebra (DE-588)4139347-8 gnd |
| topic_facet | Mathematics Matrix theory Global analysis (Mathematics) Linear and Multilinear Algebras, Matrix Theory Analysis Mathematik Dreieckszerlegung Triangulation Matrizenalgebra |
| url | https://doi.org/10.1007/978-1-4612-1200-3 |
| work_keys_str_mv | AT radjaviheydar simultaneoustriangularization AT rosenthalpeter simultaneoustriangularization |