书籍详情
MATLAB线性代数简明教程（Linear Algebra Using MATLAB）
作者：李爽 著
出版社：化学工业出版社
出版时间：2020-01-01
ISBN：9787122353214
定价：¥32.00
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内容简介
《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、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。
作者简介
李爽，武汉大学，副教授，长期从事数字图像处理、遥感图像分析与解译、离散数学、线性代数相关的教学工作。研究方向为遥感数字图像预处理、分割、分类、图像质量评价。
目录
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
6.3Cramer’s 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
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
6.3Cramer’s 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
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