A First Course in Linear Algebra is an introduction to the basic concepts of linear algebra, along with an introduction to the techniques of formal mathematics. It begins with systems of equations and matrix algebra before moving into the theory of abstract vector spaces, eigenvalues, linear transformations and matrix representations. It has numerous worked examples and exercises, along with precise statements of definitions and complete proofs of every theorem, making it ideal for independent study.
Conditions of Use
This book is licensed under a Creative Commons License (CC BY-NC-SA). You can download the ebook A First Course in Linear Algebra for free.
- Title
- A First Course in Linear Algebra
- Publisher
- Congruent Press
- Author(s)
- Robert A Beezer
- Published
- 2012-12-05
- Edition
- 3
- Format
- eBook (pdf, epub, mobi)
- Pages
- 542
- Language
- English
- ISBN-10
- 0984417559
- ISBN-13
- 9780984417551
- License
- CC BY-NC-SA
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
A First Course in Linear Algebra Preface Dedication and 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 Archetypes ABCDEFGHIJKLM NOPQRSTUVWX Reference Notation Definitions Theorems Diagrams Examples Sage Proof Techniques GFDL License
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