This accessible book for beginners uses intuitive geometric concepts to create abstract algebraic theory with a special emphasis on geometric characterizations. The book applies known results to describe various geometries and their invariants, and presents problems concerned with linear algebra, such as in real and complex analysis, differential equations, differentiable manifolds, differential geometry, Markov chains and transformation groups. The clear and inductive approach makes this book unique among existing books on linear algebra both in presentation and in content.

Part 2: The Euclidean Structures of ℝ1, ℝ2 and ℝ3 Chapter 4 The Euclidean Plane ℝ2 Chapter 5 The Euclidean Space ℝ3 Appendix Contents of Vloume One Errata to Volume One References Index of Notations Index

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