Linear Algebra and Space Analytic Geometry

Teaching Semesters

• 2026 Spring, 2025 Spring, 2024 Spring, 2023 Spring, 2022 Spring, 2021 Spring.

Acknowledgement

I gratefully acknowledge Pearson for kindly providing me with complimentary sample copies of their textbooks for my teaching. I appreciate their trust and support. These resources have informed the development of some of my personal teaching materials below.

Personal Teaching Materials & Resources

Supplementary Notes on Textbooks and References

• Textbook: David Lay’s Linear Algebra and Its Applications
  • Editions 5th and 6th are both acceptable for use, as discrepancies between them are minimal.
  • The course structure (sequence) is based on the 5th Edition (US Edition, blue cover). There is also a global edition (orange cover), which is almost identical with only minor adjustments to a few exercises and examples.
  • The 6th Edition is the latest update of the textbook, with some minor adjustments to the first 8 chapters (e.g., the order of certain topics), while the core content remains unchanged. It also includes two new chapters: Chapter 9 Optimization and Chapter 10 Finite-State Markov Chains. These chapters are interesting and useful, but they will not be covered in this course.
  • The 5th Global Edition is available as a reprint (the most cost-effective choice), and a Chinese translated version is also available.
• For more reference recommendations, check out my Study Resources & Advice page.

Personal Slides

This version was carefully adapted for my actual lectures, refined to reflect my teaching style and the needs of my students. The modifications include reworded explanations, added examples, exercises, and annotated notes to support classroom use. Copyright © Xiaozhou Li — CC BY-NC-ND 4.0

Note: Minor updates or in-class adjustments may not be reflected here in real time; slides are usually updated after each chapter is completed.

• Chapter 0. Introduction Slide

• Chapter 1. Linear Equations in Linear Algebra
  • 1.1 System of Linear Equations Slide
  • 1.2 Row Reduction and Echelon Forms Slide
  • 1.3 Vector Equations Slide
  • 1.4 The Matrix Equation Ax = b Slide
  • 1.5 Solution Sets of Linear Systems Slide
• Chapter 2. Matrix Algebra
  • 2.1 Matrix Operations Slide
  • 2.2 The Inverse of a Matrix Slide
  • 2.3 Characterizations of Invertible Matrices Slide
  • 2.4 Partitioned Matrices Slide
• Chapter 3. Determinants
  • 3.1 Introduction to Determinants Slide
  • 3.2 Properties of Determinants Slide
  • 3.3 Cramer’s Rule, Volume, and Linear Transformations Slide
• Chapter 4. Vector Spaces
  • 4.1 Vector Spaces and Subspaces Slide
  • 4.2 Null Spaces, Column Spaces, and Linear Transformations Slide
  • 4.3 Linearly Independent Sets; Bases Slide
  • 4.4 Coordinate Systems Slide
  • 4.5 The Dimension of a Vector Space Slide
  • 4.6 Rank Slide
• Chapter 5. Eigenvalues and Eigenvectors
  • 5.1 Eigenvectors and Eigenvalues Slide
  • 5.2 The Characteristic Equation Slide
  • 5.3 Diagnoalization Slide
  • 5.4 Eigenvectors and Linear Transformations Slide
• Chapter 6. Orthogonality and Least Squares
  • 6.1 Inner Product, Length, and Orthogonality Slide
  • 6.2 Orthogonal Sets Slide
  • 6.3 Orthogonal Projections Slide
  • 6.4 The Gram-Schmidt Process Slide
• Chapter 7. Symmetric Matrices and Quadratic Forms
  • 7.1 Diagonalization of Symmetric Matrices Slide
  • 7.2 Quadratic Forms Slide
• Chapter 8*. Space Analytical Geometry
  • 8.1* Planes and Lines Slide
  • 8.2* Positional Relation and Distance Slide

Supplementary Learning Materials

• 线性代数中英术语：源自《线性代数及其应用（原书第5版）》附录，仅作课程教学辅助，若涉侵权请联系本人删除。
• Problem Sets: A curated collection of problems from my courses, designed to deepen your understanding and sharpen your problem-solving skills.
• More Comprehensive Support：For general study tips, course-specific advice, and academic guidance, you can also refer to my Study Resources & Advice