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Interactive Linear Algebra
UoN Edition
Dan Margalit, Joseph Rabinoff, Ben Williams, Ulrik Buchholtz
Interactive Linear Algebra
Colophon
Contributors to this textbook
History of the UoN edition
Overview
1
Vectors: Algebra and Geometry
Vectors
Vector Equations and Spans
2
Systems of Linear Equations: Algebra
Systems of Linear Equations
Row Reduction
Parametric Form
Matrix Equations
3
Solution Sets and Subspaces
Solution Sets
Linear Independence
Subspaces
Basis and Dimension
Bases as Coordinate Systems
The Rank Theorem
Sums and Intersections of Subspaces
4
Linear 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
5
Determinants
Determinants: Definition
Cofactor Expansions
Determinants and Volumes
6
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
The Characteristic Polynomial
Similarity
Diagonalization
Complex Eigenvalues
7
Graphs and probability theory
Basic Graph Theory
Probability Theory
Discrete Dynamical Systems
Stochastic Matrices and the Steady State
8
Orthogonality
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
Colophon
Index
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Appendix
E
Hints and Solutions to Selected Exercises
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