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Interactive Linear Algebra
Dan Margalit, Joseph Rabinoff
Front Matter
Colophon
Contributors to this textbook
Variants of this textbook
Overview
1
Systems of Linear Equations: Algebra
Systems of Linear Equations
Row Reduction
Parametric Form
2
Systems 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
3
Linear Transformations and Matrix Algebra
Matrix Transformations
One-to-one and Onto Transformations
Linear Transformations
Matrix Multiplication
Matrix Inverses
The Invertible Matrix Theorem
4
Determinants
Determinants: Definition
Cofactor Expansions
Determinants and Volumes
5
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
The Characteristic Polynomial
Similarity
Diagonalization
Complex Eigenvalues
Stochastic Matrices
6
Orthogonality
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
Colophon
Index
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Appendix
C
Hints and Solutions to Selected Exercises
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