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Interactive Linear Algebra

Dan Margalit, Joseph Rabinoff

Front Matter

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Contributors to this textbook
Variants of this textbook
Overview

1Systems of Linear Equations: Algebra

Systems of Linear Equations
Row Reduction
Parametric Form

2Systems of Linear Equations: Geometry

Vectors
Vector Equations and Spans
Matrix Equations
Solution Sets
Linear Independence
Subspaces
Basis and Dimension
Bases as Coordinate Systems
The Rank Theorem

3Linear Transformations and Matrix Algebra

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

4Determinants

Determinants: Definition
Cofactor Expansions
Determinants and Volumes

5Eigenvalues and Eigenvectors

Eigenvalues and Eigenvectors
The Characteristic Polynomial
Similarity
Diagonalization
Complex Eigenvalues
Stochastic Matrices

6Orthogonality

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

Back Matter

Complex Numbers
Notation
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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