《线性代数及其应用(高校转型发展系列教材)》由潘桔、张萍、石丽云编著。
Based on the transformation development of the university, and combined with the actual situation of bilingual teaching of linear algebra, this English textbook is written by us. In this book , the needs of understanding and abilities of using the basic knowledge of linear algebra are presented, and interesting applications in other areas are emphasized. In addition, a powerful tool for matrix computations MATLAB which is easy to learn is introduced.
The contents of this textbook are derided into 6 chapters: matrices, determinants, vector spaces, eigenvalues and eigenvectors, linear transformations and MATLAB. This book is suitable for a sophomore - level course, and it is also for people who are interested in it. It pays more attention to the theory with practice and conforms to the requirements of the development of the transformation of the university. This book is suitable for bilingual teaching of linear algebra of engineering, science (not mathematics ), economic management and other related majors in ordinary higher institutions.

Chapter 1 Matrices
1.1 Basic Concepts of Matrix
1.1.1 Definition of Matrix
1.1.2 Special Matrices
1.1.3 Application Examples
1.2 Operations of Matrices
1.2.1 Linear operations of matrices
1.2.2 Multiplication of Matrices
1.2.3 Transpose of a Matrix
1.2.4 Application Examples
1.3 Matrix Inverses
1.3.1 Invertible Matrices
1.3.2 Orthogonal Matrices
1.4 Blocks of Matrices
1.4.1 Block Operations
1.4.2 Block diagonal matrices
1.5 Elementary Operations and Gauss-Jordan Elimination
1.5.1 Elementary Operations
1.5.2 Gauss-Jordan Elimination
1.6 Elementary Matrices and a Method for Finding A-1
1.6.1 Elementary Matrices
1.6.2 A Method for Finding A-1
MATLAB EXERCISES
Chapter 2 Determinants
2.1 Introduction to Determinants
2.1.1 Definitions of Determinants
2.1.2 On the Row(Column) Expansion
2.2 Properties and Evaluation of Determinants
2.2.1 Properties
2.2.2 Evaluation
2.3 Applications of Determinants
2.3.1 Adjugate Matrices and Inverse Formula
2.3.2 Cramer' s rule
2.3.3 Application Examples
MATLAB EXERCISES
Chapter 3 Vector Spaces and Linear Systems
3.1 Linear Dependence and Independence
3.2 Vector Spaces
3.2.1 Definition and Examples
3.2.2 Subspaces
3.2.3 The span of a set of vectors
3.3 Basis and Dimension
3.4 Rank
3.5 Structure for Linear Systems Solution Set
3.5.1 Homogeneous Systems
3.5.2 Non-Homogeneous Systems
MATLAB EXERCISES
Chapter 4 Eigenvalues and Eigenvectors
4.1 The Concepts of Eigenvalues and Eigenvectors
4.2 Diagonalization
4.3 Quadratic Forms and Positive Definite Matrices
MATLAB EXERCISES
Chapter 5 Linear Transformations
5.1 Definition and Examples
5.2 Matrix Representations of Linear Transformations
MATLAB EXERCISES
Chapter 6 MATLAB
6.1 Input and Output in MATLAB
6.2 Matrix Operations in MATLAB
6.2.1 Addition and Multiplication of Matrices
6.2.2 Backslash or Matrix Left Division
6.2.3 Exponentiation
6.3 Elementary Row Operations in MATLAB
6.4 Matrix Inverses in MATLAB
6.5 Vectors in MATLAB
6.6 Linear Combinations in MATLAB
6.6.1 The linear combination problem
6.6.2 The span problem
6.6.3 The linear independencedependence problem
6.7 Linear Transformations in MATLAB
6.8 MATLAB Functions
6.8.1 Programming Features I
6.8.2 M-files
6.9 Relational and Logical Operators
6.10 Columnwise Array Operators
6.11 Graphics
Bibliography