Linear Algebra
A Geometric Approach
Seiten
1993
CRC Press (Verlag)
978-0-412-40680-5 (ISBN)
CRC Press (Verlag)
978-0-412-40680-5 (ISBN)
This is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other.
The text is divided into two parts: Part I is on linear algebra and affine geometry, finishing with a chapter on transformation groups; Part II is on quadratic forms and their geometry (Euclidean geometry), including a chapter on finite subgroups of 0 (2).
Each of the 23 chapters concludes with a generous helping of exercises, and a selection of these have solutions at the end of the book. The chapters also contain many examples, both numerical worked examples (mostly in 2 and 3 dimensions), as well as examples which take some of the ideas further. Many of the chapters contain "complements" which develop more special topics, and which can be omitted on a first reading. The structure of the book is designed to allow as much flexibility as possible in designing a course, either by omitting whole chapters or by omitting the "complements" or specific examples.
The text is divided into two parts: Part I is on linear algebra and affine geometry, finishing with a chapter on transformation groups; Part II is on quadratic forms and their geometry (Euclidean geometry), including a chapter on finite subgroups of 0 (2).
Each of the 23 chapters concludes with a generous helping of exercises, and a selection of these have solutions at the end of the book. The chapters also contain many examples, both numerical worked examples (mostly in 2 and 3 dimensions), as well as examples which take some of the ideas further. Many of the chapters contain "complements" which develop more special topics, and which can be omitted on a first reading. The structure of the book is designed to allow as much flexibility as possible in designing a course, either by omitting whole chapters or by omitting the "complements" or specific examples.
E. Sernesi
Part I Affine geometry: vector spaces; matrices; systems of linear equations; some linear algebra; rank; determinants; affine space - (I) - (II); geometry of affine planes; geometry of affine space; linear maps; linear maps and matrices, affine changes of coordinates; linear operators; transformation groups. Part II Euclidean geometry: bilinear and quadratic forms; diagonalizing quadratic forms; scalar product; vector product; Euclidean space; unitary operators and isometries; isometries of the plane and of three-dimensional space; the complex case.
| Erscheint lt. Verlag | 15.5.1993 |
|---|---|
| Reihe/Serie | Chapman Hall/CRC Mathematics Series |
| Verlagsort | London |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 710 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-412-40680-2 / 0412406802 |
| ISBN-13 | 978-0-412-40680-5 / 9780412406805 |
| Zustand | Neuware |
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