Linear algebra

Author: Wang Naixin
Publisher:
Publish Date: 2002-07-01
Features: This book is a research outcome of the Ministry of Education's "Reform Plan for Teaching Content and Curriculum Systems in Higher Education Towards the 21st Century," serving as a curriculum textbook for the 21st century and a "Nineth Five-Year Plan" teaching material for the agricultural and forestry mathematics discipline under the Ministry of Education. This textbook introduces fundamental concepts of linear algebra by starting with the representation, solution, and analysis of systems of linear algebraic equations. It emphasizes the perspective of linear transformations, using this viewpoint to explain systems of linear algebraic equations, matrices and their various operations, eigenvalues and eigenvectors, and the transformation of quadratic forms into standard forms. Appropriate examples are selected to reveal the background and essence of the concepts, making them clearer. The textbook also highlights elementary row operations, employing these methods to solve systems of linear algebraic equations, determine the linear dependence of vector sets and their ranks, perform matrix inversion, and find eigenvalues and eigenvectors. This simplifies computational techniques, making the solutions more standardized and concise. Additionally, the content on determinants is reduced, some minor proofs are omitted, and the application of linear algebra is strengthened, with a dedicated chapter on application examples and another on numerical methods examples. This book is suitable for use as a teaching material in higher agricultural and forestry institutions.