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.
Rezensionen / Stimmen
"Written in a clear and readable style, this text can be recommended to every student, who is interested to see the beautiful connections between Algebra and Geometry and to learn the necessary notions and theorems in order to understand it."
-Monatshefte fir mathematik
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Maße
Höhe: 234 mm
Breite: 156 mm
Dicke: 20 mm
Gewicht
ISBN-13
978-0-412-40680-5 (9780412406805)
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Schweitzer Klassifikation
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.
