Home

• Preface
• Acknowledgments

Systems of Linear Equations

• What is Linear Algebra?
• Solving Systems of Linear Equations
• Reduced Row-Echelon Form
• Types of Solution Sets
• Homogeneous Systems of Equations
• Nonsingular Matrices

Vectors

• Vector Operations
• Linear Combinations
• Spanning Sets
• Linear Independence
• Linear Dependence and Spans
• Orthogonality

Matrices

• Matrix Operations
• Matrix Multiplication
• Matrix Inverses and Systems of Linear Equations
• Matrix Inverses and Nonsingular Matrices
• Column and Row Spaces
• Four Subsets

Vector Spaces

• Vector Spaces
• Subspaces
• Linear Independence and Spanning Sets
• Bases
• Dimension
• Properties of Dimension

Determinants

• Determinant of a Matrix
• Properties of Determinants of Matrices

Eigenvalues

• Eigenvalues and Eigenvectors
• Properties of Eigenvalues and Eigenvectors
• Similarity and Diagonalization

Linear Transformations

• Linear Transformations
• Injective Linear Transformations
• Surjective Linear Transformations
• Invertible Linear Transformations

Representations

• Vector Representations
• Matrix Representations
• Change of Basis
• Orthonormal Diagonalization
• Nilpotent Linear Transformations
• Invariant Subspaces
• Jordan Canonical Form

Appendices

Preliminaries

• Complex Number Operations
• Sets
• Proof Techniques

Archetypes

•     A B C D E F G H
•     I J K L M N O P
•     Q R S T P V W X

GNU Free Documentation License

 
 
 
© 2004 by Robert A. Beezer.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the appendix entitled “GNU Free Documentation License”.

 
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