Introduction to the authors of Linear Algebra Practice and Introduction to MATLAB

About author:Professor Chen Huaichen graduated from Zhangjiakou Military Telecommunications Engineering College (now Xidian University) in 1953, stayed on to teach, and taught more than 10 courses in the Department of Mechanical Engineering, the Department of Automatic Control and the Department of Electronic Engineering. In 1980, he went to the Department of Systems Engineering at the University of Pennsylvania in Philadelphia

After returning to China, he served as the vice president of Xidian University, in charge of scientific research and graduate education, and concurrently served as the director of the Chinese Association of Automation.

Since 1995, Professor Chan has been promoting the computerization of university curricula and teaching, with the aim of enabling both faculty and students to use computers instead of calculators to solve computational problems in their courses. He has presided over the compilation of a series of textbooks that apply MATLAB to university courses, such as "CAD and MATLAB Language for Control Systems", "Digital Signal Processing and Its Implementation in MATLAB", "MATLAB and Its Application Guide in Science and Engineering Courses", "MATLAB and Its Application in Electronic Information Courses", and "Digital Signal Processing Tutorial - MATLAB Interpretation and Implementation".

Resources.

Exercise 1:1, subtract the number of rows from the matrix, that is, subtract the minimum number in the data of each row to obtain matrix two;

2. Check matrix two, if each row and column of matrix two has 0, skip this step, otherwise carry out column approximation, that is, sell each column of data minus the minimum value in this column of data to obtain matrix three;

Note: It is also possible to reduce the line of the line first and then reduce the line.

3. Draw the "cover 0" line, that is, draw the least line to cover all the 0 in matrix 3 to get matrix 4;

Tip: Start with the row or column with the most 0s and draw the "cover 0" line.

4. Data conversion. If the number of "cover 0" lines is equal to the dimension of the matrix, skip this step, and if the number of "cover 0" lines is less than the dimension of the matrix, the data conversion is performed. If this problem belongs to the latter, the optimal solution is directly solved.

For the n-dimensional matrix, find n zeros in different rows and columns, and the position of each 0 represents a pair of configuration relationships, the specific steps are as follows.

1) First find a row (or column) with only a 0 in the ruler, and hit the 0 in the row (or column) with "".

2) Place the 0 with " " in the row (or column) where the other 0 is hit "".

3) Repeat steps (1) and (2) to the end. If all rows and columns contain more than one 0, choose a dozen "" from the row or column with the least number of zeros

Exercise 2: (Same solution as Exercise 1).

1. Perform row reduction and subtraction of the matrix, that is, each row of data subtracts the minimum number in the data of the bank to obtain matrix two;

2. Check matrix two, if each row and column of matrix two have 0, skip this step, otherwise the column is reduced approximately, that is, each column of data subtracts the minimum value in the data in this column to obtain matrix three;

Note: It is also possible to reduce the line of the line first and then reduce the line.

3. Draw the "cover 0" line, that is, draw the least line to cover all the 0 in matrix 3 to get matrix 4;

Tip: Start with the row or column with the most 0s and draw the "cover 0" line.

4. Data conversion. If the number of "cover 0" lines is equal to the dimension of the matrix, skip this step, and if the number of "cover 0" lines is less than the dimension of the matrix, the data conversion is performed. If this problem belongs to the latter, the optimal solution is directly solved.

For the n-dimensional matrix, find n zeros in different rows and columns, and the position of each 0 represents a pair of configuration relationships, the specific steps are as follows.

1) Find a row (or column) that contains only one 0, and tick the 0 in the row (or column) with "".

2) Place the 0 with " " in the row (or column) where the other 0 is hit "".

3) Repeat steps (1) and (2) to the end. If all rows and columns contain more than one 0, choose a dozen "" from the row or column with the least number of zeros

The first edition of this book is a supplementary textbook on linear algebra compiled according to the guiding ideology of "using software tools to improve the teaching of linear algebra" and with reference to the idea of atlast of the National Science ** Project in the United States from 1992 to 1997. It is divided into two parts, the first of which introduces the software tool used in linear algebra, the MATLAB language, which can be used as a textbook or as a manual; The second part introduces the practice of linear algebra, including three aspects: first, the visualization function of MATLAB is used to give a geometric image to the concepts in linear algebra; second, it provides concise algorithms and programs for tedious calculations in linear algebra; Third, a large number of examples of the use of linear algebra modeling in various engineering and economic fields are given.

The second edition of this book adds Chapter 10 to the revision of the first edition, expanding on more than 10 examples of deeper matrix modeling and solving in subsequent courses in the Mechanics and Electronics major.

This book can not only be used as a supporting textbook for undergraduate linear algebra, but also as a reference book for teachers, engineers, senior undergraduates and graduate students in the fields of science and engineering, economics and management to learn matrix modeling and master its computer solutions.

This book can be used in conjunction with the textbook Linear Algebra (Fourth Edition) edited by the Department of Applied Mathematics of Tongji University. This book provides some guidance for students who are studying and reviewing linear algebra, helps students deepen their understanding of the basic concepts and theorems in linear algebra, guides students to master the problem-solving methods and skills of linear algebra, and inspires and cultivates students' interest in learning linear algebra.