Elementary Linear Algebra Textbook

Author: Li XuHong
Publisher:
Publish Date: 2003-10-01
Features: A novel "Elementary Linear Algebra Textbook," explaining the fundamental theorems of linear algebra in a new way, uncovering the black holes in mathematics, allowing you to experience philosophical discussions and easily learn linear algebra methods. This book is organized around the fundamental theorems, establishing a new theoretical framework for linear dependence, adding some new theorems, and improving the proofs of certain theorems. It introduces the concept of determinants through the discovery method, provides a standard formulation of Cramer's Rule along with a new proof, and highlights that Cramer's Rule is a fundamental rule with significant theoretical importance. The discussions are philosophical, such as exploring the philosophy of numbers and the symmetry of beauty. The book is well-organized, making it easy to teach; the explanations are thorough, facilitating understanding; and the steps are detailed, ensuring readability. Each chapter includes a summary, and the exercises come with answers. It enables self-learners to study independently and helps beginners enter the subject effortlessly. This book provides sufficient material for students from non-mathematics backgrounds to learn linear algebra, making it suitable for students of various disciplines and needs in different schools. Even for mathematics majors, it is highly beneficial. At the end of the book, there is an appendix titled "Miscellaneous Notes on Advanced Mathematics," which includes ten of my works dedicated to readers studying advanced mathematics. Some of these articles can serve as supplements to textbooks, offering inspiration and novelty.