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Interactive Linear AlgebraUoN Edition

Dan Margalit, Joseph Rabinoff, Ben Williams, Ulrik Buchholtz

Interactive Linear Algebra

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Contributors to this textbook
History of the UoN edition
Overview

1Vectors: Algebra and Geometry

Vectors
Vector Equations and Spans

2Systems of Linear Equations: Algebra

Systems of Linear Equations
Row Reduction
Parametric Form
Matrix Equations

3Solution Sets and Subspaces

Solution Sets
Linear Independence
Subspaces
Basis and Dimension
Bases as Coordinate Systems
The Rank Theorem
Sums and Intersections of Subspaces

4Linear Transformations and Matrix Algebra

Matrix Transformations
One-to-one and Onto Transformations
Linear Transformations
Matrix Multiplication
Matrix Inverses
The Invertible Matrix Theorem
Invertible matrices and Coordinate Systems

5Determinants

Determinants: Definition
Cofactor Expansions
Determinants and Volumes

6Eigenvalues and Eigenvectors

Eigenvalues and Eigenvectors
The Characteristic Polynomial
Similarity
Diagonalization
Complex Eigenvalues

7Graphs and probability theory

Basic Graph Theory
Probability Theory
Discrete Dynamical Systems
Stochastic Matrices and the Steady State

8Orthogonality

Dot Products and Orthogonality
Orthogonal Complements
Orthogonal Projection
Orthogonal Sets
The Method of Least Squares

Back Matter

Complex Numbers
Fields and Vector Spaces
Notation
Concept Library
Hints and Solutions to Selected Exercises
GNU Free Documentation License
Index
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This book was authored in MathBook XML, with modifications by Rabinoff.

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