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Interactive Linear Algebra
UBC edition
Dan Margalit, Joseph Rabinoff, Ben Williams
Front Matter
Colophon
Contributors to this textbook
History of the UBC 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
4
Linear Transformations and Matrix Algebra
Matrix Transformations
One-to-one and Onto Transformations
Linear Transformations
Matrix Multiplication
Matrix Inverses
The Invertible Matrix Theorem
5
Determinants
Determinants: Definition
Cofactor Expansions
Determinants and Volumes
6
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
The Characteristic Polynomial
Similarity
Diagonalization
Complex Eigenvalues
Discrete dynamical systems
Stochastic Matrices and the Steady State
7
Orthogonality
Dot Products and Orthogonality
Orthogonal Complements
Orthogonal Projection
Orthogonal Sets
The Method of Least Squares
Back Matter
Complex Numbers
Notation
GNU Free Documentation License
Index
Colophon
Index
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Back Matter
ΒΆ permalink
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Complex Numbers
B
Notation
C
GNU Free Documentation License
Index
Colophon
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