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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.
Sample Chapter(s)
Part 1: The A.ne and Linear Structures of R1, R2 and R3 (170 KB)
Contents:
- The Affine and Linear Structures of P1, P2 and P3:
- The One-Dimensional Real Vector Space P (or P1)
- The Two-Dimensional Real Vector Space P2
- The Three-Dimensional Real Vector Space P3
Readership: Upper-level undergraduates, graduate students and lecturers.
