Linear Algebra Lecture Notes

Author: Shi Guangyan
Publisher:
Publish Date: 2004-06-01
Features: This book is compiled from the lecture notes of Shi Guangyan Professor's postgraduate entrance exam tutoring. It covers the content required for undergraduate teaching and the postgraduate entrance exam syllabus, including all types of questions in the exam. The summary of knowledge points is concise, thorough, and the selection of examples aims to guide the understanding of concepts, the grasp of relationships, the formation of problem-solving approaches, and the application of knowledge points. Target Audience: Undergraduate students studying Linear Algebra, postgraduate entrance exam candidates, and university teachers. While learning knowledge, attention should also be paid to the cultivation of abilities. The development of abilities relies not only on the accumulation of knowledge but also requires conscious effort. In the limited classroom time, teachers can help students develop this awareness by leveraging their broader knowledge base and the experience of creative thinking to refine the course content, capturing its essence, and providing key insights during discussions of problem posing and problem solving. The book consists of 7 chapters and 20 teaching hours, with each chapter setting goals for knowledge and ability development. I am an elderly teaching and research worker. Looking back on my university days, one of the courses I took was Advanced Mathematics, with the main content being calculus and differential equations. This was a very important course. As a worker, looking back on my university days, one of the courses I took was Advanced Mathematics, with the main content being calculus and differential equations. This was a very important course. Over the decades of my career, it has been this foundation that has supported me. However, I have also always felt that, whether in learning or research, once we have a mathematical model or equation for a problem, it remains unsolvable due to computational difficulties in solving it. Later, in the early 1960s, with the advent of electronic computers, they entered various fields of engineering and technology, bringing bright prospects. Many computational difficulties could then be solved with the help of computers. As a result, new disciplines such as computational mathematics, computational mechanics, and computational physics emerged. Many problems could be solved by discretizing mathematical models and equations on computers.