Linear Algebra and Projective Geometry (Dover Books on Mathematics) by Reinhold Baer (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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:[…]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.

⭐very good book

⭐The book makes a systematic approach to show that linear algebra and projective geometry are mathematically equivalent.This is important for higher studies and research.

⭐The plot’s a bit convoluted and the characterisation’s a bit thin. I’d still love to see the movie though. They’d be lots of 3D wireframe graphics getting stretched out of shape all the time.

⭐

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