线性代数(英文维基教科书)
The book was designed specifically for students who had not previously been exposed to mathematics as mathematicians view it. That is, as a subject whose goal is to rigorously prove theorems starting from clear consistent definitions. This book attempts to build students up from a background where mathematics is simply a tool that provides useful calculations to the point where the students have a grasp of the clear and precise nature of mathematics. A more detailed discussion of the prerequisites and goal of this book is given in the introduction.
这本书是专门为那些以前没有接触过数学的学生设计的,因为他们是数学家。也就是说,作为一个目标是从清晰一致的定义开始严格证明定理的学科。这本书试图建立学生从一个背景,数学只是一个工具,提供有用的计算点,学生有一个清晰和精确的数学性质的掌握。引言中对本书的先决条件和目标进行了更详细的讨论。
这本教科书翻译自英文维基教科书Linear Algebra,相关的翻译问题可见讨论页。
Table of Contents 目录 编辑
Linear Systems 线性方程组 编辑
- Solving Linear Systems 求解线性方程组 (2020年12月9日)
- Linear Geometry of n-Space
- Reduced Echelon Form
- Topic: Computer Algebra Systems
- Topic: Input-Output Analysis
- Input-Output Analysis M File
- Topic: Accuracy of Computations
- Topic: Analyzing Networks
- Topic: Speed of Gauss' Method
Vector Spaces 编辑
- Definition of Vector Space
- Linear Independence
- Basis and Dimension
- Topic: Fields
- Topic: Crystals
- Topic: Voting Paradoxes
- Topic: Dimensional Analysis
Maps Between Spaces 编辑
- Isomorphisms
- Homomorphisms
- Computing Linear Maps
- Matrix Operations
- Change of Basis
- Projection
- Topic: Line of Best Fit
- Topic: Geometry of Linear Maps
- Topic: Markov Chains
- Topic: Orthonormal Matrices
Determinants 编辑
- Definition
- Geometry of Determinants
- Other Formulas for Determinants
- Topic: Cramer's Rule
- Topic: Speed of Calculating Determinants
- Topic: Projective Geometry
Similarity 编辑
- Complex Vector Spaces
- Similarity
- Nilpotence
- Jordan Form
- Topic: Geometry of Eigenvalues
- Topic: The Method of Powers
- Topic: Stable Populations
- Topic: Linear Recurrences
Unitary Transformations 编辑
Appendix 编辑
Resources and Licensing 编辑
- Licensing And History
- Resources
- Bibliography (see individual pages for references)
- Index