Linear algebra, analytic geometry

Author: Yang Qitian Dai Jun
Publisher:
Publish Date: 2002-10-01
Features: This book systematically introduces the fundamental theories and methods of linear algebra and analytical geometry, with particular emphasis on the integration and connection between algebra and geometry. Based on providing geometric context, it strengthens the teaching of linear spaces and their linear transformations, placing them as core content earlier in the book to allow readers to encounter axiomatic definitions and methods at an early stage, laying a foundation for learning modern mathematics. The book is divided into 9 chapters: Vector Operations · Planes and Lines, Determinants of Square Matrices · Systems of Linear Equations, Matrices and Their Operations, Linear Spaces, Linear Transformations, Euclidean Spaces, Common Surfaces, Quadratic Forms, and an Introduction to Basic Concepts of Abstract Algebra. Chapter 9 introduces the fundamental concepts of groups, rings, and fields, which are optional content. Each chapter concludes with a summary and is accompanied by a certain number of exercises, including fill-in-the-blank and multiple-choice questions. This book can serve as a textbook and teaching reference for non-mathematics majors in higher education institutions, as well as a reference for self-learners and related personnel.