Linear Geometry (Dover Books on Mathematics) - Softcover

Artzy, Rafael; Mathematics

Softcover

ISBN 10: 0486466272 ISBN 13: 9780486466279

Publisher: Dover Publications, 2008

Synopsis

Most linear algebra texts neglect geometry in general and linear geometry in particular. This text for advanced undergraduates and graduate students stresses the relationship between algebra and linear geometry. It begins by using the complex number plane as an introduction to a variety of transformations and their groups in the Euclidean plane, explaining algebraic concepts as they arise. A brief account of Poincaré's model of the hyperbolic plane and its transformation group follow.
Succeeding chapters contain a systematic treatment of affine, Euclidean, and projective spaces over fields that emphasizes transformations and their groups, along with an outline of results involving other geometries. An examination of the foundations of geometry starts from rudimentary projective incidence planes, then gradually adjoins axioms and develops various non-Desarguesian, Desarguesian, and Pappian planes, their corresponding algebraic structures, and their collineation groups. The axioms of order, continuity, and congruence make their appearance and lead to Euclidean and non-Euclidean planes. Lists of books for suggested further reading follow the third and fourth chapters, and the Appendix provides lists of notations, axioms, and transformation groups.

About this edition

• Publisher: Dover Publications
• Publication date: 2008
• ISBN 10: 0486466272
• ISBN 13: 9780486466279
• Binding: Paperback
• Edition number: 3
• Number of pages: 288