Li Yongle, male, is a famous expert in linear algebra. Professor, Department of Applied Mathematics, Tsinghua University, Vice Chairman of Mathematics Research Association of Beijing Higher Education Society.
He used to be the head of the national postgraduate entrance examination Beijing mathematics marking group. He participated in the revision of the mathematics syllabus for postgraduate entrance examination and the proposition work of the national mathematics examination for many times and was received by the leaders of the Ministry of Education.
Teacher Li Yongle compiled many reference books on mathematics for postgraduate entrance examination, which enjoyed a high reputation among candidates and were out of stock year after year. Teacher Li knows the questions and the key points of the exam like the back of his hand. His thinking of solving problems is extremely flexible, and his counseling is highly targeted, with excellent results and remarkable achievements. He was praised by the students!
As an independent branch discipline, linear algebra has a long history, although it was only formed in the 20th century. The problem of "chicken and rabbit in the same cage" is actually a simple problem of solving linear equations.
The oldest linear problem is the solution of linear equations, which has been completely described in the ancient Chinese mathematical work "Nine Chapters Arithmetic Equations", and the method in it is essentially equivalent to the elementary transformation of rows of the augmented matrix of modern equations and the method of eliminating unknowns.
Due to the work of Fermat and Descartes, linear algebra in the modern sense basically appeared in the seventeenth century. Until the end of18th century, the field of linear algebra was limited to plane and space. /kloc-completed the transition to n-dimensional linear space in the first half of the 9th century.
With the in-depth study of linear equations and linear transformation of variables, determinant and matrix came into being in the period of 18 ~ 19 century, which provided powerful tools for dealing with linear problems and promoted the development of linear algebra.
The introduction of the concept of vector forms the concept of vector space. All linear problems can be discussed from the viewpoint of vector space. Therefore, vector space and its linear transformation, as well as the related matrix theory, constitute the central content of linear algebra.
Matrix theory began in Gloria, and reached its peak in the second half of the 9th century because of Jordan's work. 1888, piano defined a linear space with finite or infinite dimensions in an axiomatic way. Toplitz extends the main theorem of linear algebra to the most general vector space in any field.
The concept of linear mapping can get rid of matrix calculation in most cases and does not depend on the choice of basis. Instead of commutative bodies, we use bodies or rings that are not necessarily commutative as the domain of operators, which leads to the concept of modules, significantly expands the theory of linear spaces, and rearranges the situation studied in19th century.
The word "algebra" appeared late in Chinese and was introduced to China in Qing Dynasty. At that time, it was translated as "Algar Barra". It was not until 1859 that Li Cai, a famous mathematician and translator in Qing Dynasty, translated it into Algebra, which has been in use ever since.