Linear Algebra
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Linear Algebra
An Introduction to Mathematical Discourse
This book requires that you are familiar with calculus. This subject is covered by the wikibook Calculus. |
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.
Table of Contents
This book is part of a series on Algebra:
Linear Systems
- Solving Linear Systems
- 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
- Definition of Vector Space
- Linear Independence
- Basis and Dimension
- Topic: Fields
- Topic: Crystals
- Topic: Voting Paradoxes
- Topic: Dimensional Analysis
Maps Between Spaces
- 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
- Definition
- Geometry of Determinants
- Other Formulas for Determinants
- Topic: Cramer's Rule
- Topic: Speed of Calculating Determinants
- Topic: Projective Geometry
Similarity
- Complex Vector Spaces
- Similarity
- Nilpotence
- Jordan Form
- Topic: Geometry of Eigenvalues
- Topic: The Method of Powers
- Topic: Stable Populations
- Topic: Linear Recurrences
Unitary Transformations
Appendix
Resources and Licensing
- Licensing And History
- Resources
- Bibliography (see individual pages for references)
- Index