本課程旨在建立學生對線性代數基本理論與方法的完整認識，培養抽象思考、邏輯推理及數學證明能力。課程內容涵蓋線性方程組、矩陣運算、行列式、向量空間、子空間、線性獨立、基底與維度、線性映射、秩與零度、特徵值與特徵向量、對角化，以及內積空間與正交化等主題。透過理論講授、例題分析與習題演練，使學生理解線性結構的基本概念及其相互關係，掌握線性代數在數學及相關領域中的核心地位。課程並強調定理證明與抽象概念的理解，為後續高等代數、微分方程、數值分析及其他進階數學課程奠定基礎。

This course aims to establish students' complete understanding of the basic theories and methods of linear algebra, and cultivate their abilities in abstract thinking, logical reasoning and mathematical proof. The course content covers topics such as systems of linear equations, matrix operations, determinants, vector spaces, subspaces, linear independence, basis and dimensions, linear mapping, rank and zero degree, eigenvalues ​​and eigenvectors, diagonalization, and inner product spaces and orthogonalization. Through theoretical lectures, example analysis and exercise exercises, students can understand the basic concepts of linear structures and their interrelationships, and master the core position of linear algebra in mathematics and related fields. The course also emphasizes theorem proving and understanding of abstract concepts, laying the foundation for subsequent advanced algebra, differential equations, numerical analysis and other advanced mathematics courses.

介紹線性代數的理論及其應用

Introduction to the theory and applications of linear algebra

Linear Algebra, 4/e, Arnold J Insel , Lawrence E. Spence , Stephen H Friedberg

Linear Algebra, 4/e, Arnold J Insel, Lawrence E. Spence, Stephen H Friedberg