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 theorems lead to a reconstruction of the geometry that constituted the discussion's starting point. 1952 edition.
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33 of 35 people found the following review helpful:
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This review is from: Linear Algebra and Projective Geometry (Dover Books on Mathematics) (Paperback)
This is not a standard linear algebra text. If you're looking for an introductory book or even a geometrical-themed supplement to an introductory book, this is NOT what you are looking for. Baer assumes you have already mastered standard linear algebra, and are quite familar with fields, groups, rings, isomorphisms, homomorphisms, Galois theory, etc. He also assumes you have a grasp of the concepts and theorems of projective (and some affine) geometry. There are no explicit exercises or problems, but more than a few non-trivial statements/theorems and non-obvious facts are left for the reader to prove or justify. The table of contents can be found at:
http://web.doverpublications.com/cgi-bin/toc.pl/0486445658 This book is a good follow-up to _Linear Algebra: A Geometric Approach_ by Sernesi (Chapman & Hall), which is "introductory" (although not really for the rank beginner) and mostly focuses on affine geometry. If you're looking for a geometric supplement for an introductory course, try _A Vector Space Approach to Geometry_ by Hausner (Dover). With those caveats out of the way, this is great book, even if upon first reading some sections are so dense that they bend light. But as you work through it, there are many moments of illumination if you have a bent for the interplay and fundamental equivalence between algebra and geometry. But it isn't spoon-fed to you.
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- Selected Papers of Wilhelm P.A. Klingenberg (Series in Pure Mathematics) by Wilhelm P. A. Klingenberg on page 240, page 243, and page 250
- Geometry II (Universitext) (v. 2) by Marcel Berger in Back Matter
- Finite Geometry and Combinatorics (London Mathematical Society Lecture Note Series) by F. de Clerck on page 205
- Real Reductive Groups I, Vol. 132 (Pure and Applied Mathematics) by Nolan R. Wallach in Index
- Fundamental Structures of Algebra and Discrete Mathematics by Stephan Foldes on page 194
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