Multilinear Algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1967
|
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete
136 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is built around the material on multilinear algebra which in chapters VI to IX of the second edition of Linear Algebra was included but excluded from the third edition. It is designed to be a sequel and companion volume to the third edition of Linear Algebra. In fact, the terminology and basic results of that book are frequently used without reference. In particular, the reader should be familiar with chapters I to V and the first part of chapter VI although other sections are occasionally used. The essential difference between the present treatment and that of the second edition lies in the full exploitation of universal properties which eliminates the restrietion to vector spaces of finite dimension. Chapter I contains standard material on multilinear mappings and the tensor product of vector spaces. These results are extended in Chapter II to vector spaces with additional structure, such as algebras and differential spaces. The fundamental concept of "tensor product" is used in Chapter III to construct the tensor algebra over a given vector space. In the next chapter the link is provided between tensor algebra on the one hand and exterior and symmetrie tensor algebra on the other. Chapter V contains material on exterior algebra which is developed in considerable depth. Exterior algebra techniques are used in the following chapter as a powerful tool to obtain matrix-free proofs of many classical theorems on linear transformation |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783662007952 9783662007976 |
| DOI: | 10.1007/978-3-662-00795-2 |
Internformat
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| 490 | 1 | |a Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |v 136 | |
| 500 | |a This book is built around the material on multilinear algebra which in chapters VI to IX of the second edition of Linear Algebra was included but excluded from the third edition. It is designed to be a sequel and companion volume to the third edition of Linear Algebra. In fact, the terminology and basic results of that book are frequently used without reference. In particular, the reader should be familiar with chapters I to V and the first part of chapter VI although other sections are occasionally used. The essential difference between the present treatment and that of the second edition lies in the full exploitation of universal properties which eliminates the restrietion to vector spaces of finite dimension. Chapter I contains standard material on multilinear mappings and the tensor product of vector spaces. These results are extended in Chapter II to vector spaces with additional structure, such as algebras and differential spaces. The fundamental concept of "tensor product" is used in Chapter III to construct the tensor algebra over a given vector space. In the next chapter the link is provided between tensor algebra on the one hand and exterior and symmetrie tensor algebra on the other. Chapter V contains material on exterior algebra which is developed in considerable depth. Exterior algebra techniques are used in the following chapter as a powerful tool to obtain matrix-free proofs of many classical theorems on linear transformation | ||
| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
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| building | Verbundindex |
| bvnumber | BV042423184 |
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| dewey-full | 510 |
| 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 | 10.1007/978-3-662-00795-2 |
| format | Electronic eBook |
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| id | DE-604.BV042423184 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:38:44Z |
| institution | BVB |
| isbn | 9783662007952 9783662007976 |
| language | English |
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| publishDate | 1967 |
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| publisher | Springer Berlin Heidelberg |
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| series | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| series2 | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Greub, Werner Hildbert 1925-1991 Verfasser (DE-588)123729912 aut Multilinear Algebra by W. H. Greub Berlin, Heidelberg Springer Berlin Heidelberg 1967 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 136 This book is built around the material on multilinear algebra which in chapters VI to IX of the second edition of Linear Algebra was included but excluded from the third edition. It is designed to be a sequel and companion volume to the third edition of Linear Algebra. In fact, the terminology and basic results of that book are frequently used without reference. In particular, the reader should be familiar with chapters I to V and the first part of chapter VI although other sections are occasionally used. The essential difference between the present treatment and that of the second edition lies in the full exploitation of universal properties which eliminates the restrietion to vector spaces of finite dimension. Chapter I contains standard material on multilinear mappings and the tensor product of vector spaces. These results are extended in Chapter II to vector spaces with additional structure, such as algebras and differential spaces. The fundamental concept of "tensor product" is used in Chapter III to construct the tensor algebra over a given vector space. In the next chapter the link is provided between tensor algebra on the one hand and exterior and symmetrie tensor algebra on the other. Chapter V contains material on exterior algebra which is developed in considerable depth. Exterior algebra techniques are used in the following chapter as a powerful tool to obtain matrix-free proofs of many classical theorems on linear transformation Mathematics Mathematics, general Mathematik Multilineare Algebra (DE-588)4416303-4 gnd rswk-swf Multilineare Algebra (DE-588)4416303-4 s 1\p DE-604 Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 136 (DE-604)BV049758308 136 https://doi.org/10.1007/978-3-662-00795-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Greub, Werner Hildbert 1925-1991 Multilinear Algebra Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete Mathematics Mathematics, general Mathematik Multilineare Algebra (DE-588)4416303-4 gnd |
| subject_GND | (DE-588)4416303-4 |
| title | Multilinear Algebra |
| title_auth | Multilinear Algebra |
| title_exact_search | Multilinear Algebra |
| title_full | Multilinear Algebra by W. H. Greub |
| title_fullStr | Multilinear Algebra by W. H. Greub |
| title_full_unstemmed | Multilinear Algebra by W. H. Greub |
| title_short | Multilinear Algebra |
| title_sort | multilinear algebra |
| topic | Mathematics Mathematics, general Mathematik Multilineare Algebra (DE-588)4416303-4 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Multilineare Algebra |
| url | https://doi.org/10.1007/978-3-662-00795-2 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT greubwernerhildbert multilinearalgebra |