Linear Algebra Fundamentals Tutorial

Author: Wang Liqin
Publisher:
Publishing Date: 2004-08-01
Features: Linear algebra is a branch of algebra primarily used for handling linear relationship problems. Vector spaces, systems of linear equations, linear transformations, and the associated matrix theory constitute the core content of linear algebra. Linear algebra has broad applications in many fields of engineering technology and the national economy, and its computational methods are an important aspect of computational mathematics.
In today's rapidly developing science and technology, the demand for mathematical foundations among professionals in various fields continues to rise. As a foundational mathematics course, linear algebra is inherently theoretical and computationally complex, often perceived as dry and abstract. How can teaching content and methods be improved to enhance student interest and motivation? How can mathematical thinking be integrated into teaching while also equipping students with the computational skills they need now and in the future? With this objective in mind, based on years of teaching experience and recent practices in computer-assisted instruction, this textbook has been written for students in various disciplines with a certain level of mathematical foundation, with the hope that it will serve as a practical resource.
This textbook is characterized by the following features:
1. Reasonable structure, smooth logic, progressing from simple to complex, clear and concise, with appropriate examples to aid understanding and provide context for the applications of linear algebra;
2. Reduced verbose proofs of theorems and derivations of formulas, with an increased number of examples;
3. Enhanced content on computer-assisted instruction, introducing the mathematical software Mathematica 4.0, enabling students to master the skills of using software for complex computations after learning the fundamental concepts, theories, and operational methods of linear algebra.
The authors of this textbook include: Wang Liqin, Li Naihua, Wang Haiming, and Hu Jian.
This textbook is suitable for undergraduate and vocational college students with limited class hours, as well as for self-study purposes as an introductory reference for linear algebra. Content marked with an asterisk can be selected based on the available course schedule.
During the writing process, this textbook referenced multiple textbooks and monographs, and some examples and exercises were adapted from them. Gratitude is expressed to all the referenced sources.