Linear algebra

Author: Ji Tianfu, Luo Rujiu (editors)
Publisher:
Publish Date: 2006-08-01
Features: Linear algebra is a fundamental mathematics course in higher vocational and technical colleges. Its concepts and methods are widely applied in scientific research, engineering technology, and the national economy. Since matrices, as the main object of study in linear algebra, are central to the entire course, linear algebra is also known as matrix theory. This book strives to reflect the teaching characteristics of higher vocational and technical colleges and adheres to the principle of "aiming at application with essential and sufficient content." In terms of structure and content, it has distinctive features. Starting from the elimination method for systems of linear equations, which students are already familiar with from middle school, it naturally introduces the important operation method of elementary row transformations of matrices and places it in a crucial position. Using elementary row transformations of matrices, the book discusses the rank of matrices, the linear dependence of vector sets, the method for finding the maximum linearly independent set, the determination and structure of solutions to linear equations, the diagonalization of matrices, and quadratic forms. The structure is compact, clear, and concise; it is both profound and accessible, making it easy to understand. The book is divided into four chapters: Chapter 1, Matrices and Determinants; Chapter 2, Vectors and the Structure of Solutions to Linear Equations; Chapter 3, Diagonalization of Matrices; Chapter 4, Quadratic Forms. After each section, there are exercises, and at the end of each chapter, there are review questions. Partial answers and hints are provided. These exercises are closely linked to the textbook content, helping to consolidate and deepen understanding of the material. If students can think independently and complete them, they will surely achieve twice the result with half the effort.