Matrix Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1979
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | These notes were developed from a course taught at Rice University in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vector-valued functions. The idea is to introduce students to some of the concepts of Lie group theory-- all done at the concrete level of matrix groups. As much as we could, we motivated developments as a means of deciding when two matrix groups (with different definitions) are isomorphie. In Chapter I "group" is defined and examples are given; homorphism and isomorphism are defined. For a field k denotes the algebra of n x n matrices over k We recall that A E Mn(k) has an inverse if and only if det A # 0 , and define the general linear group GL(n,k) We construct the skew-field E of quaternions and note that for A E Mn(E) to operate linearly on Rn we must operate on the right (since we multiply a vector by a scalar n n on the left). So we use row vectors for Rn, c E and write xA , for the row vector obtained by matrix multiplication. We get a complex-valued determinant function on Mn (E) such that det A # 0 guarantees that A has an inverse |
| Beschreibung: | 1 Online-Ressource (XII, 191p) |
| ISBN: | 9781468400939 9780387904627 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4684-0093-9 |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-0093-9 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468400939 9780387904627 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856418 |
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| publishDate | 1979 |
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| spelling | Curtis, Morton L. Verfasser aut Matrix Groups by Morton L. Curtis New York, NY Springer US 1979 1 Online-Ressource (XII, 191p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 These notes were developed from a course taught at Rice University in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vector-valued functions. The idea is to introduce students to some of the concepts of Lie group theory-- all done at the concrete level of matrix groups. As much as we could, we motivated developments as a means of deciding when two matrix groups (with different definitions) are isomorphie. In Chapter I "group" is defined and examples are given; homorphism and isomorphism are defined. For a field k denotes the algebra of n x n matrices over k We recall that A E Mn(k) has an inverse if and only if det A # 0 , and define the general linear group GL(n,k) We construct the skew-field E of quaternions and note that for A E Mn(E) to operate linearly on Rn we must operate on the right (since we multiply a vector by a scalar n n on the left). So we use row vectors for Rn, c E and write xA , for the row vector obtained by matrix multiplication. We get a complex-valued determinant function on Mn (E) such that det A # 0 guarantees that A has an inverse Mathematics Mathematics, general Mathematik Matrizengruppe (DE-588)4169127-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf Matrizengruppe (DE-588)4169127-1 s 1\p DE-604 Gruppentheorie (DE-588)4072157-7 s 2\p DE-604 Matrizenrechnung (DE-588)4126963-9 s 3\p DE-604 https://doi.org/10.1007/978-1-4684-0093-9 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 |
| spellingShingle | Curtis, Morton L. Matrix Groups Mathematics Mathematics, general Mathematik Matrizengruppe (DE-588)4169127-1 gnd Gruppentheorie (DE-588)4072157-7 gnd Matrizenrechnung (DE-588)4126963-9 gnd |
| subject_GND | (DE-588)4169127-1 (DE-588)4072157-7 (DE-588)4126963-9 |
| title | Matrix Groups |
| title_auth | Matrix Groups |
| title_exact_search | Matrix Groups |
| title_full | Matrix Groups by Morton L. Curtis |
| title_fullStr | Matrix Groups by Morton L. Curtis |
| title_full_unstemmed | Matrix Groups by Morton L. Curtis |
| title_short | Matrix Groups |
| title_sort | matrix groups |
| topic | Mathematics Mathematics, general Mathematik Matrizengruppe (DE-588)4169127-1 gnd Gruppentheorie (DE-588)4072157-7 gnd Matrizenrechnung (DE-588)4126963-9 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Matrizengruppe Gruppentheorie Matrizenrechnung |
| url | https://doi.org/10.1007/978-1-4684-0093-9 |
| work_keys_str_mv | AT curtismortonl matrixgroups |