《MATLAB线性代数简明教程Linear Algebra Using MATLAB》共分为8章，主要内容为：第1章介绍了MATLAB软件的桌面和MATLAB编程基础，第2章～第7章分别介绍了线性代数的各种运算，包括矩阵运算、求解线性方程、向量空间和子空间、投影、*小二乘逼近、行列式、特征值和特征向量、相似矩阵和奇异值分解等。此外，基于图像处理与线性代数有着密切的关系，第8章简要介绍了线性代数在图像处理中的应用。本书结合线性代数理论与MATLAB语言介绍线性代数的应用，列举了丰富的MATLAB代码实例，不仅可以加深对线性代数理论的理解，而且可以提高应用线性代数知识解决实际问题的能力。
《MATLAB线性代数简明教程Linear Algebra Using MATLAB》可作为高等院校理工科专业基础课教材，也是运用MATLAB语言与数学知识解决实际问题的工具书，可供从事经济、物理、系统控制、信号处理、图像处理等领域专业技术人员参考。
《MATLAB线性代数简明教程Linear Algebra Using MATLAB》共分为8章，主要内容为：第1章介绍了MATLAB软件的桌面和MATLAB编程基础，第2章～第7章分别介绍了线性代数的各种运算，包括矩阵运算、求解线性方程、向量空间和子空间、投影、*小二乘逼近、行列式、特征值和特征向量、相似矩阵和奇异值分解等。此外，基于图像处理与线性代数有着密切的关系，第8章简要介绍了线性代数在图像处理中的应用。本书结合线性代数理论与MATLAB语言介绍线性代数的应用，列举了丰富的MATLAB代码实例，不仅可以加深对线性代数理论的理解，而且可以提高应用线性代数知识解决实际问题的能力。
《MATLAB线性代数简明教程Linear Algebra Using MATLAB》可作为高等院校理工科专业基础课教材，也是运用MATLAB语言与数学知识解决实际问题的工具书，可供从事经济、物理、系统控制、信号处理、图像处理等领域专业技术人员参考。
Chapter 1Fundament for MATLAB1
1.1MATLAB Desktop1
1.2Vectors and Matrices7
1.3MATLAB Programming11
Chapter 2Introduction to Vectors and Matrices20
2.1Vectors and Linear Combination20
2.2Lengths and Dot Products28
2.3Matrices31
Chapter 3Solving Linear Equations40
3.1Vectors and Linear Equations40
3.2The Idea of Elimination45
3.3Elimination Using Matrices52
3.4Inverse Matrices58
Chapter 4Vector Spaces and Subspaces62
4.1Spaces of Vectors62
4.2The Nullspace of matrix64
4.3The Rank and Linear Dependence68
Chapter 5Orthogonality71
5.1 Projections71
5.2Least Squares Approximations75
5.3Orthogonal Bases and Gram-Schmidt Process80
Chapter 6Determinants85
6.1 The Properties of Determinants85
6.2Permutations and Cofactors92
6.3Cramers Rule98
Chapter 7Eigenvalues and Eigenvectors102
7.1Introduction to Eigenvalues102
7.2Similar matrices and diagonalization of matrices105
7.3Singular Value Decomposition109
Chapter 8Linear Algebra in Image Processing112
8.1Digital Image Representation112
8.2Geometric Transformation using Matrix Operation114
8.3Image Restoration using Inverse Matrix117
8.4Image Fusion using Principal Component Analysis119
8.5Image Compression using Singular Value Decomposition120
References122
內容試閱：
前言
欢迎使用《MATLAB线性代数简明教程Linear Algebra Using MATLAB》这本书。线性代数是高等院校理工科专业的重要基础课，也是运用数学知识解决实际问题的有力工具，广泛应用于经济、物理、系统控制、信号处理、图像处理等领域。线性代数对逻辑推理、抽象思维和基本运算的能力要求较高。在学习线性代数之后，读者应该知道如何用数学方法解决实际问题，并使用计算机进行科学计算。 而本书采用MATLAB语言解决线性代数问题。MATLAB（MATrix LABoratory，矩阵实验室）软件源于矩阵运算。作为一种高度集成的计算机语言，拥有大量的工具箱，具有强大的科学运算能力、灵活的编程过程和高质量的图形可视化能力。另外，MATLAB软件与其他编程语言的接口也非常方便。
本书首先介绍了MATLAB软件的桌面和MATLAB编程基础第1章，然后介绍了线性代数的各种运算第2章～第7章，包括矩阵运算、求解线性方程、向量空间和子空间、投影、最小二乘逼近、行列式、特征值和特征向量、相似矩阵和奇异值分解等。此外，由于图像可以看作矩阵，对图像的运算实际上就是对矩阵的运算。故基于图像处理与线性代数有着密切的关系，最后介绍了线性代数在图像处理中的应用第8章。本书结合线性代数理论与MATLAB语言介绍线性代数的应用，列举了丰富的MATLAB代码实例，不仅可以加深对线性代数理论的理解，而且可以提高应用线性代数知识解决实际问题的能力。你会发现学习线性代数最有效的方式就是使用这本教材。
在此，我们感谢对本书提出宝贵意见的专家，特别感谢化学工业出版社编辑的大力支持。我们还感谢武汉大学2016级本科生董志斌、黄宇卓和霍启正，他们参加了部分文字的输入和程序调试工作。本书的编写和出版得到了国家自然科学基金（编号：41901357，编号：41701394）的资助。在此，编者向资助的提供者表示诚挚的谢意。
尽管我们为编写本书付出了很多的努力，但由于学识水平的限制，本书对一些问题的理解和解释难免存在不妥之处，敬请读者批评指正。如对本书有任何意见及建议，请与编者联系，邮箱：sli@whu.edu.cn。
编者
2019年9月
Preface
Welcome to Linear Algebra Using MATLAB.Linear algebra is an important basic course for science and technology majors in universities and also is a powerful tool to solve practical problems with mathematical knowledge，which is widely used in economy，physics，system control，signal processing，image processing and so on.Linear algebra requires your ability of logical reasoning，abstract thinking and basic operation.After learning linear algebra，you should know how to solve practical problems with mathematical methods，and use computers to carry out certain scientific calculations.This book focuses on solving linear algebra problems with software.MATLAB（the abbreviation for MATrix LABoratory）software originated from matrix operation.As a highly integrated computer language，MATLAB possesses plenty of toolboxes and provides ability of powerful scientific operations，flexible programming process，and high-quality graphics visualization.In addition，MATLAB software is also very convenient to interface with other programming languages.Thus，MATLAB language is adopted to solve the linear algebra problems in this book.
We first present the guide to MATLAB desktop and fundament to MATLAB programming.Then we introduce various operations of linear algebra using MATLAB，including matrix operation，solving linear equations，vector space and subspace，projections，least square approximation，determinants，eigenvalues and eigenvectors，similar matrices，and singular value decomposition.As colorful image can be treated as multi-dimensional matrix，the operation on image is actually the operation on matrix，which is closely related to linear algebra.Finally，we will give plenty of applications of linear algebra in image processing.This book integrates the theory of linear algebra，the application of linear algebra and the software of MATLAB.The abundant examples can not only deepen the understanding of linear algebra theory，but also improve the ability to apply linear algebra knowledge to solve practical problems.You will be learning the language of linear algebra in the best and most efficient way：by using it.
We are grateful to the many reviewers who helped us shape and refine Linear Algebra Using MATLAB.We also give special thanks to the people at Chemical Industry Press who worked with us in the development of Linear Algebra Using MATLAB.We also thank undergraduate student Zhibin Dong，Yuzhuo Huang and Qizheng Huo from grade 2016 in Wuhan University，who assisted with the development of the code.This book is supported by the project National Natural Science Foundation of China（No.41901357，No.41701394）.We are also grateful to our sponsors.
We have worked hard to make Linear Algebra Using MATLAB，a useful and practical textbook from which to teach and learn linear algebra.Despite our best efforts to ensure accuracy of use，many users will undoubtedly have suggestions for improvement.We welcome your suggestions.The contact email address is sli@whu.edu.cn.
Editor in Chief
2019.9
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