This was the teaching material of computational mathematics specialty at that time, and it was said that the teaching requirements were higher than the corresponding courses of mathematics specialty. Because it is biased towards calculation, we can find some commonly used algorithms. Personally, I think it's quite interesting.
2. Advanced algebra, etc.
This is the one about advanced algebra in a set of Fudan Mathematics Department textbooks published by Shanghai Science and Technology. 80% of this book is devoted to the theory of matrices. There are many exercises, especially the multiple-choice questions at the end of each chapter. It is very beneficial to understand the various properties of matrix to complete the exercises independently. Of course, this is not easy: it is said that when Mr. Tu retired, he left a sentence: If anyone opens Advanced Algebra and uses this book as a teaching material in the future, he can come to me if he has difficulties in exercises. This shows that if you think the above book is too bad from the perspective of exercises, then the following book should be said to be more suitable.
3. Tu Bojun et al. "Linear Algebra-Method Guidance"
This book may be easier to find and more practical than the one above. It's worth doing.
4. Xu Yichao's linear algebra and matrix theory
This book is well written and well practiced. It must be pointed out that it actually attaches great importance to the concept of space. Anyway, he is still a disciple of Mr. Hua.
5. Hua "Introduction to Advanced Mathematics" Mr. Hua's mathematical research is characterized by unique elementary methods and intuitive methods, and he has also made great achievements in matrix theory. In Gunter Maher's book, you
China people can only find two names, one is Mr Ky Fan and the other is Mr Hua. This may be the first time that he introduced the following ideas into China's mathematics textbooks.
(I don't remember if it is in this book): The determinant of order n is the only antisymmetric linear function that maps a set of standard bases to 1 on the Cartesian product of n N-dimensional linear spaces. This is very close to the viewpoint of multilinear algebra or tensor analysis.
6. Qiu Advanced Algebra (I and II)
The textbook of Peking University Grade 94 is quite good. It is characterized by comprehensiveness. Although it is not as in-depth as the above-mentioned books in the direction of matrix, it is very clear in space theory, specifically some geometric ideas. Polynomial theory is also talked a lot.
7. Li Jiongsheng, Cha Jianguo's Linear Algebra
This is the textbook of the Chinese University of Science and Technology, which may have inherited some traditions of Mr. Hua. Some of its contents may be quite advanced in China.
This book is "the most difficult book in Asia" in advanced algebra.
8. Advanced Algebra revised by Wang Efang.
This book was written by the primary array of the Geometry and Algebra Teaching and Research Section of Peking University Mathematics Department. The third edition was revised by Wang Yifang and Shi Shengming. It is a teaching material for undergraduates majoring in mathematics in many universities, and it is also a reference for entrance examinations of advanced algebra or linear algebra for graduate students in many universities.
9. Xu Advanced Algebra
The main content of higher algebra is linear algebra, including number and polynomial, determinant, linear equations, matrix, linear space, quadratic form, linear transformation, space decomposition, matrix similarity, Euclidean space and unitary space, bilinear form; The course content includes orthogonal geometry and symplectic geometry, Hilbert space, tensor product and outer product. The content is profound and convenient for readers to lay a favorable foundation. The viewpoint is novel and it is convenient for readers to adapt to modern mathematics. There are also some introductory contents, which can be used as teaching materials for science and engineering majors such as mathematics, physics, computer and electronic information in colleges and universities, and can also be used as reference for other majors.
10. Du Xiankun, formerly known as Permanent, edited by Niu.
Press: Higher Education Press
This book is a textbook for undergraduates majoring in mathematics in colleges and universities, including the standard contents of advanced algebra courses: polynomial, determinant, linear equations, matrix theory, vector space and its linear transformation, quadratic form, bilinear form and so on. In particular, the content of matrix standard form is strengthened. This book strives to be concise and easy to understand, and pays attention to the connection between elementary algebra and advanced algebra, advanced algebra and other subsequent courses. This book can also be used as a reference for teachers and students of science and engineering.
1 1. By Gao
Publishing House: Tsinghua University Publishing House
Advanced algebra is a basic course for mathematics majors in colleges and universities, and it is also the basic content of postgraduate entrance examination. Based on years of teaching experience, this book strives to make every basic concept have a realistic background, so that students can easily accept those abstract objects. The book focuses on the basic clues and thinking methods, so that students can look at what they have learned on a higher platform. This book introduces unary polynomial, determinant, matrix, linear equations, linear space, linear transformation and quadratic form. It can be used as a teaching material for all majors in the department of mathematics in comprehensive universities and normal universities, and also as a reference book for teachers and mathematicians in the department of mathematics in colleges and universities.
I think this is probably the most authoritative book on matrix theory. The translator is Mr. Ke Zhao. In this two-volume book, there are many things that are not in the textbooks at ordinary times. For example, we all know that a matrix has Jordan standard, but how to find the transformation matrix from a matrix to its Jordan standard? Please look at the matrix theory. There are some interesting discussions about matrix equations in this book.
2. N. Jacobson's Lectures on Abstract Algebra, II: Linear Algebra GTM (Mathematics Graduate Textbook) No.31
(Abstract Algebra Volume II: Linear Algebra)
What I want to say here is that the Chinese translator of this set of books, Mr. Huang, probably not many people in the Department of Mathematics remember that there was such an algebra professor in Fudan before the Cultural Revolution.
3. Linear Algebra (GTM23)
In fact, it is more about multilinear algebra. Some of these chapters are worth reading.