*Linear Algebra*

Linear Algebra is a featured book on Wikibooks because it contains substantial content, it is well-formatted, and the Wikibooks community has decided to feature it on the main page or in other places. Please continue to improve it and thanks for the great work so far! You can edit its advertisement template. |

*Linear Algebra*

*An Introduction to Mathematical Discourse*

This book requires that you are familiar with calculus. This subject is covered by the wikibook Calculus. |

This book discusses *proof-based* linear algebra. The book was designed specifically for students who have 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.

Because of the proof-based nature of this book, readers are recommended to be familiar with mathematical proof before reading this book (although this is not a prerequisite, strictly speaking), so that their reading experiences can be smoother. To gain familiarity with mathematical proof and also some basic mathematical concepts, readers may read the wikibook Mathematical Proof. For a milder introduction to linear algebra that is not too *proof-based*, see the wikibook Introductory Linear Algebra.

## 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

The following is a brief overview of some basic concepts in mathematics. For more details, reader can read the wikibook Mathematical Proof.

### Resources and Licensing

- Licensing And History
- Resources
- Bibliography (see individual pages for references)
- Index