Linear Algebra with Python and AI
暫譯: 使用 Python 和 AI 的線性代數

This book is a compelling and accessible introduction to linear algebra, ideal for learners and educators across mathematics, data science, engineering, and the physical sciences. It begins with core topics such as systems of linear equations, matrix operations, and Row-Reduced Echelon Form (RREF), and builds a coherent pathway toward advanced concepts like eigenvalues, inner product spaces, and singular value decomposition (SVD). With a clear pedagogical structure and consistent notation, the text supports both conceptual understanding and practical application.What sets this textbook apart is its seamless integration of theory and computation. Python (NumPy/SymPy) is used throughout to implement algorithms, visualize geometric ideas, and connect abstract mathematics to real-world problems. Carefully designed TikZ diagrams enhance geometric intuition, while applications such as least squares, data compression, and principal component analysis (PCA) demonstrate the relevance of linear algebra in modern fields. Integrated coding examples and computational tools encourage hands-on exploration and foster algorithmic thinking.Whether you're mastering Gaussian elimination, exploring the Rank-Nullity Theorem, or experimenting with Python notebooks, Linear Algebra with Python and AI offers a unified and forward-looking approach. With its dual emphasis on mathematical rigor and computational practice, this book equips students with the tools to navigate the mathematical foundations of today's data-driven world.