Geometric Linear Algebra

Description:

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.

 

Table of 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

 

描述：
這本適合初學者的易懂書籍使用直觀的幾何概念來創建抽象代數理論，特別強調幾何特徵。該書應用已知結果來描述各種幾何和它們的不變量，並提出與線性代數有關的問題，例如在實數和複數分析、微分方程、可微流形、微分幾何、馬爾可夫鏈和變換群中。清晰且歸納的方法使得這本書在呈現和內容上都與現有的線性代數書籍不同。

目錄：
- 第一章：ℝ¹、ℝ²和ℝ³的仿射和線性結構
- 第二章：一維實向量空間ℝ（或ℝ¹）
- 第三章：二維實向量空間ℝ²
- 第四章：三維實向量空間ℝ³