A First Course in Linear Algebra

by
Robert A. Beezer
Department of Mathematics and Computer Science
University of Puget Sound

Version 1.01

© 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 the Invariant Sections being “Preface”, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the appendix entitled “GNU Free Documentation License”.
The most recent version of this work can always be found at http://linear.ups.edu.

Front Matter
 Author Biography
 Edition
 Publisher
 Dedication
Contributors
Definitions
Theorems
Notation
Examples
Preface
Acknowledgements
Part C Core
Chapter SLE Systems of Linear Equations
 Section WILA What is Linear Algebra?
 Section SSLE Solving Systems of Linear Equations
 Section RREF Reduced Row-Echelon Form
 Section TSS Types of Solution Sets
 Section HSE Homogeneous Systems of Equations
 Section NM Nonsingular Matrices
Chapter V Vectors
 Section VO Vector Operations
 Section LC Linear Combinations
 Section SS Spanning Sets
 Section LI Linear Independence
 Section LDS Linear Dependence and Spans
 Section O Orthogonality
Chapter M Matrices
 Section MO Matrix Operations
 Section MM Matrix Multiplication
 Section MISLE Matrix Inverses and Systems of Linear Equations
 Section MINM Matrix Inverses and Nonsingular Matrices
 Section CRS Column and Row Spaces
 Section FS Four Subsets
Chapter VS Vector Spaces
 Section VS Vector Spaces
 Section S Subspaces
 Section LISS Linear Independence and Spanning Sets
 Section B Bases
 Section D Dimension
 Section PD Properties of Dimension
Chapter D Determinants
 Section DM Determinant of a Matrix
 Section PDM Properties of Determinants of Matrices
Chapter E Eigenvalues
 Section EE Eigenvalues and Eigenvectors
 Section PEE Properties of Eigenvalues and Eigenvectors
 Section SD Similarity and Diagonalization
Chapter LT Linear Transformations
 Section LT Linear Transformations
 Section ILT Injective Linear Transformations
 Section SLT Surjective Linear Transformations
 Section IVLT Invertible Linear Transformations
Chapter R Representations
 Section VR Vector Representations
 Section MR Matrix Representations
 Section CB Change of Basis
 Section NLT Nilpotent Linear Transformations
 Section IS Invariant Subspaces
 Section JCF Jordan Canonical Form
Appendix CN Computation Notes
 Section MMA Mathematica
 Section TI86 Texas Instruments 86
 Section TI83 Texas Instruments 83
Appendix P Preliminaries
 Section CNO Complex Number Operations
 Section SET Sets
 Section PT Proof Techniques
Appendix A Archetypes
 Archetype A
 Archetype B
 Archetype C
 Archetype D
 Archetype E
 Archetype F
 Archetype G
 Archetype H
 Archetype I
 Archetype J
 Archetype K
 Archetype L
 Archetype M
 Archetype N
 Archetype O
 Archetype P
 Archetype Q
 Archetype R
 Archetype S
 Archetype T
 Archetype U
 Archetype V
 Archetype W
 Archetype X
Appendix GFDL GNU Free Documentation License
  1. APPLICABILITY AND DEFINITIONS
  2. VERBATIM COPYING
  3. COPYING IN QUANTITY
  4. MODIFICATIONS
  5. COMBINING DOCUMENTS
  6. COLLECTIONS OF DOCUMENTS
  7. AGGREGATION WITH INDEPENDENT WORKS
  8. TRANSLATION
  9. TERMINATION
  10. FUTURE REVISIONS OF THIS LICENSE
  ADDENDUM: How to use this License for your documents
Part T Topics
 Section F Fields
Part A Applications
Index