Linear Algebra Through Geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer US
1983
|
| Series: | Undergraduate Texts in Mathematics
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | In this book we lead the student to an understanding of elementary linear algebra by emphasizing the geometric significance of the subject. Our experience in teaching beginning undergraduates over the years has convinced us that students learn the new ideas of linear algebra best when these ideas are grounded in the familiar geometry of two and three dimensions. Many important notions of linear algebra already occur in these dimensions in a non-trivial way, and a student with a confident grasp of these ideas will encounter little difficulty in extending them to higher dimensions and to more abstract algebraic systems. Moreover, we feel that this geometric approach provides a solid basis for the linear algebra needed in engineering, physics, biology, and chemistry, as well as in economics and statistics. The great advantage of beginning with a thorough study of the linear algebra of the plane is that students are introduced quickly to the most important new concepts while they are still on the familiar ground of two-dimensional geometry. In short order, the student sees and uses the notions of dot product, linear transformations, determinants, eigenvalues, and quadratic forms. This is done in Chapters 2.0-2.7. Then the very same outline is used in Chapters 3.0-3.7 to present the linear algebra of three-dimensional space, so that the former ideas are reinforced while new concepts are being introduced |
| Physical Description: | 1 Online-Ressource (X, 257p. 81 illus) |
| ISBN: | 9781468401615 9781468401639 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-1-4684-0161-5 |
Staff View
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Record in the Search Index
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| any_adam_object | |
| author | Banchoff, Thomas |
| author_facet | Banchoff, Thomas |
| author_role | aut |
| author_sort | Banchoff, Thomas |
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| 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 |
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| id | DE-604.BV042421011 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468401615 9781468401639 |
| issn | 0172-6056 |
| language | English |
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| physical | 1 Online-Ressource (X, 257p. 81 illus) |
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| publishDate | 1983 |
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| publisher | Springer US |
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| series2 | Undergraduate Texts in Mathematics |
| spelling | Banchoff, Thomas Verfasser aut Linear Algebra Through Geometry by Thomas Banchoff, John Wermer New York, NY Springer US 1983 1 Online-Ressource (X, 257p. 81 illus) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 In this book we lead the student to an understanding of elementary linear algebra by emphasizing the geometric significance of the subject. Our experience in teaching beginning undergraduates over the years has convinced us that students learn the new ideas of linear algebra best when these ideas are grounded in the familiar geometry of two and three dimensions. Many important notions of linear algebra already occur in these dimensions in a non-trivial way, and a student with a confident grasp of these ideas will encounter little difficulty in extending them to higher dimensions and to more abstract algebraic systems. Moreover, we feel that this geometric approach provides a solid basis for the linear algebra needed in engineering, physics, biology, and chemistry, as well as in economics and statistics. The great advantage of beginning with a thorough study of the linear algebra of the plane is that students are introduced quickly to the most important new concepts while they are still on the familiar ground of two-dimensional geometry. In short order, the student sees and uses the notions of dot product, linear transformations, determinants, eigenvalues, and quadratic forms. This is done in Chapters 2.0-2.7. Then the very same outline is used in Chapters 3.0-3.7 to present the linear algebra of three-dimensional space, so that the former ideas are reinforced while new concepts are being introduced Mathematics Matrix theory Geometry Linear and Multilinear Algebras, Matrix Theory Mathematik Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Vektorrechnung (DE-588)4062471-7 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Geometrie (DE-588)4020236-7 s 1\p DE-604 Analytische Geometrie (DE-588)4001867-2 s 2\p DE-604 Vektorrechnung (DE-588)4062471-7 s 3\p DE-604 Algebraische Geometrie (DE-588)4001161-6 s 4\p DE-604 Wermer, John Sonstige oth https://doi.org/10.1007/978-1-4684-0161-5 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 |
| spellingShingle | Banchoff, Thomas Linear Algebra Through Geometry Mathematics Matrix theory Geometry Linear and Multilinear Algebras, Matrix Theory Mathematik Analytische Geometrie (DE-588)4001867-2 gnd Geometrie (DE-588)4020236-7 gnd Lineare Algebra (DE-588)4035811-2 gnd Vektorrechnung (DE-588)4062471-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4001867-2 (DE-588)4020236-7 (DE-588)4035811-2 (DE-588)4062471-7 (DE-588)4001161-6 |
| title | Linear Algebra Through Geometry |
| title_auth | Linear Algebra Through Geometry |
| title_exact_search | Linear Algebra Through Geometry |
| title_full | Linear Algebra Through Geometry by Thomas Banchoff, John Wermer |
| title_fullStr | Linear Algebra Through Geometry by Thomas Banchoff, John Wermer |
| title_full_unstemmed | Linear Algebra Through Geometry by Thomas Banchoff, John Wermer |
| title_short | Linear Algebra Through Geometry |
| title_sort | linear algebra through geometry |
| topic | Mathematics Matrix theory Geometry Linear and Multilinear Algebras, Matrix Theory Mathematik Analytische Geometrie (DE-588)4001867-2 gnd Geometrie (DE-588)4020236-7 gnd Lineare Algebra (DE-588)4035811-2 gnd Vektorrechnung (DE-588)4062471-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Mathematics Matrix theory Geometry Linear and Multilinear Algebras, Matrix Theory Mathematik Analytische Geometrie Geometrie Lineare Algebra Vektorrechnung Algebraische Geometrie |
| url | https://doi.org/10.1007/978-1-4684-0161-5 |
| work_keys_str_mv | AT banchoffthomas linearalgebrathroughgeometry AT wermerjohn linearalgebrathroughgeometry |