A First Course in Linear Algebra
Robert A. Beezer
A First Course in Linear Algebra
Free
Description
Contents
Reviews

This book is a well-organized text with carefully constructed examples, a full quota of exercises with solutions, and an emphasis that is algebraic rather than geometric. The book is Sage-enabled with approximately 90 examples of Sage code spread throughout. The book sections can be loaded into Sage as worksheets so that the code can be evaluated immediately; however, it is not necessary to use Sage in order to make use of this textbook.

The HTML version is a fully featured electronic text with cross references that expand in place. It works well on an iPad or any device with Internet access. The Sage examples are executed by the Sage single cell server over the Internet, and students can experiment with their own examples as they read without needing to install Sage or log into a Sage server. Most students will prefer this version over both the pdf and print versions.

As stated in the preface of the book, the dual aims are “to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics.”

Verion 3.50 (spring 2016) is archived here. Online and Hardcover versions are available via the author's website.

Language
English
ISBN
978-0-9844175-5-1
Preface
Acknowledgements
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
Preliminaries
Complex Number Operations
Sets
Reference
Proof Techniques
Archetypes
Definitions
Theorems
Notation
GNU Free Documentation License
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