前言

歡迎使用《MATLAB線性代數(shù)簡明教程(Linear Algebra Using MATLAB)》這本書。線性代數(shù)是高等院校理工科專業(yè)的重要基礎(chǔ)課，也是運用數(shù)學(xué)知識解決實際問題的有力工具，廣泛應(yīng)用于經(jīng)濟、物理、系統(tǒng)控制、信號處理、圖像處理等領(lǐng)域。線性代數(shù)對邏輯推理、抽象思維和基本運算的能力要求較高。在學(xué)習(xí)線性代數(shù)之后，讀者應(yīng)該知道如何用數(shù)學(xué)方法解決實際問題，并使用計算機進行科學(xué)計算。 而本書采用MATLAB語言解決線性代數(shù)問題。MATLAB（MATrix LABoratory，矩陣實驗室）軟件源于矩陣運算。作為一種高度集成的計算機語言，擁有大量的工具箱，具有強大的科學(xué)運算能力、靈活的編程過程和高質(zhì)量的圖形可視化能力。另外，MATLAB軟件與其他編程語言的接口也非常方便。

本書首先介紹了MATLAB軟件的桌面和MATLAB編程基礎(chǔ)(第1章)，然后介紹了線性代數(shù)的各種運算(第2章～第7章)，包括矩陣運算、求解線性方程、向量空間和子空間、投影、最小二乘逼近、行列式、特征值和特征向量、相似矩陣和奇異值分解等。此外，由于圖像可以看作矩陣，對圖像的運算實際上就是對矩陣的運算。故基于圖像處理與線性代數(shù)有著密切的關(guān)系，最后介紹了線性代數(shù)在圖像處理中的應(yīng)用(第8章)。本書結(jié)合線性代數(shù)理論與MATLAB語言介紹線性代數(shù)的應(yīng)用，列舉了豐富的MATLAB代碼實例，不僅可以加深對線性代數(shù)理論的理解，而且可以提高應(yīng)用線性代數(shù)知識解決實際問題的能力。你會發(fā)現(xiàn)學(xué)習(xí)線性代數(shù)最有效的方式就是使用這本教材。

在此，我們感謝對本書提出寶貴意見的專家，特別感謝化學(xué)工業(yè)出版社編輯的大力支持。我們還感謝武漢大學(xué)2016級本科生董志斌、黃宇卓和霍啟正，他們參加了部分文字的輸入和程序調(diào)試工作。本書的編寫和出版得到了國家自然科學(xué)基金（編號：41901357，編號：41701394）的資助。在此，編者向資助的提供者表示誠摯的謝意。

盡管我們?yōu)榫帉懕緯�付出了很多的努力，但由于學(xué)識水平的限制，本書對一些問題的理解和解釋難免存在不妥之處，敬請讀者批評指正。如對本書有任何意見及建議，請與編者聯(lián)系，郵箱：sli@whu.edu.cn。



編者

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