作者介紹
(美)吉爾伯特·斯特朗|責編:張子堯
吉爾伯特·斯特朗（Gilbert Strang），美國享有盛譽的數學家、教育家，在有限元理論、變分法、小波分析和線性代數等方面皆有研究貢獻。他對數學教育做出了許多貢獻，出版了十幾部數學教科書和專著。曾任麻省理工學院數學系MathWorks講座教授。主要講授「線性代數導論」「計算科學與工程」等開放式課程，獲得廣泛好評，是美國數學開放教學的領軍人物。曾任美國數學聯合政策委員會主席、美國數學委員會主席、美國國家科學基金會（NSF）數學顧問小組主席、國際工業與應用數學理事會（ICIAM）理事、阿貝爾獎委員會委員等職務。2009年當選美國國家科學院院士。在麻省理工學院任教61年後，他開設的MIT 18.06課程（線性代數）在OCW（開放式課程）平台上瀏覽量超過1000萬次。
目錄
CHAPTER 1 Matrices and Gaussian Elimination
1.1 Introduction
1.2 The Geometry of Linear Equations
1.3 An Example of Gaussian Elimination
1.4 Matrix Notation and Matrix Multiplication
1.5 Triangular Factors and Row Exchanges
1.6 Inverses and Transposes
1.7 Special Matrices and Applications
CHAPTER 2 Vector Spaces
2.1 Vector Spaces and Subspaces
2.2 Solving Ax=0 and Ax=b
2.3 Linear Independence, Basis, and Dimension
2.4 The Four Fundamental Subspaces
2.5 Linear Transformations
CHAPTER 3 Orthogonality
3.1 Orthogonal Vectors and Subspaces
3.2 Cosines and Projections onto Lines
3.3 Projections and Least Squares
3.4 Orthogonal Bases and Gram–Schmidt
3.5 The Fast Fourier Transform
CHAPTER 4 Determinants
4.1 Introduction
4.2 Properties of the Determinant
4.3 Formulas for the Determinant
4.4 Applications of Determinants
CHAPTER 5 Eigenvalues and Eigenvectors
5.1 Introduction
5.2 Diagonalization of a Matrix
5.3 Difference Equations and Powers A^{k}
5.4 Differential Equations and e^{At}
5.5 Complex Matrices
5.6 Similarity Transformations
CHAPTER 6 Positive Definite Matrices
6.1 Minima, Maxima, and Saddle Points
6.2 Tests for Positive Definiteness
6.3 Singular Value Decomposition
6.4 Minimum Principles
6.5 The Finite Element Method
APPENDIX A Intersection, Sum, and Product of Spaces
APPENDIX B The Jordan Form
Matrix Factorizations
Linear Algebra in a Nutshell
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