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.

Contents:

• The Affine and Linear Structures of ℝ¹, ℝ² and ℝ³:
• The One-Dimensional Real Vector Space ℝ (or ℝ¹)
• The Two-Dimensional Real Vector Space ℝ²
• The Three-Dimensional Real Vector Space ℝ³

“The clear and inductive approach makes this book unique among existing books on linear algebra both in presentation and in content.”