Linear Algebra and Projective Geometry: Pure and Applied Mathematics, V2 - Softcover

Baer, Reinhold

Softcover

ISBN 10: 1258668890 ISBN 13: 9781258668891

Publisher: Literary Licensing, LLC, 2013

Synopsis

Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point, within algebraic structures such as the endomorphism ring of the underlying manifold or the full linear group.
Restricted to topics of an algebraic nature, the text shows how far purely algebraic methods may extend. It assumes only a familiarity with the basic concepts and terms of algebra. The methods of transfinite set theory frequently recur, and for readers unfamiliar with this theory, the concepts and principles appear in a special appendix.

Edition details

• Publisher: Literary Licensing, LLC
• Publication date: 2013
• ISBN 10: 1258668890
• ISBN 13: 9781258668891
• Binding: Paperback
• Language: English
• Number of pages: 326
• Editor: Smith Paul A, Eilenberg Samuel