# A First Course in Linear Algebra

Robert Beezer, University of Puget Sound

Pub Date: 2008

ISBN 13:

Publisher: University of Puget Sound

Language: English

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## Reviews

This book contains a standard set of topics one would expect to see in a first semester Linear Algebra course, beginning with systems of linear equations and transitioning into vectors and matrices. Abstract vector spaces appear in the middle of... read more

If anything, this textbook is too comprehensive: it exhaustively covers all linear algebra canon. read more

This is a great book that covers most topics that should be included in an introductory linear algebra course. In fact, many of the topics are discussed in more depth than what is necessary for an intro course. The Reading Questions at the end of... read more

I examined this book carefully last semester while searching for a good inexpensive (or free) textbook to adopt for a sophomore-level linear algebra course. This book contains all the topics that I'd normally cover in such a course, plus more. The... read more

There is a lot of great basic material here. However, there are several topics missing that I would consider part of a standard first course in linear algebra. Matrix factorizations, such as the Cholesky factorization, or decompositions, such as... read more

The text covers all the topics of a first course in linear algebra. There is discussion on set theory, complex numbers and proof techniques. Complex number are mentioned very early in the text although not used. Very little emphasis on the... read more

This book includes a good selection of topics for a semester-long linear algebra course. read more

This book covers a tiny bit more than I would normally cover in an introductory linear algebra class (due to its use of the complex numbers throughout), and omits nothing that I would normally cover. All subject areas address in the Table of... read more

Beezer's book includes all the expected topics in a first corse in linear algebra, and it also provides some review sections on set theory and complex numbers. To place it in the broader world of linear algebra textbooks, this text is generally... read more

## Table of Contents

- Chapter SLE Systems of Linear Equations
- Chapter V Vectors
- Chapter M Matrices
- Chapter VS Vector Spaces
- Chapter D Determinants
- Chapter E Eigenvalues
- Chapter LT Linear Transformations
- Chapter R Representations
- Chapter MD Matrix Decompositions
- Appendix CN Computation Notes
- Appendix P Preliminaries
- Appendix A Archetypes
- Appendix GFDL GNU Free Documentation License
- Part T Topics
- Section F Fields
- Section T Trace
- Section HP Hadamard Product
- Section VM Vandermonde Matrix
- Section PSM Positive Semi-definite Matrices
- Part A Applications
- Section CF Curve Fitting
- Section SAS Sharing A Secret
- Index

## About the Book

*A First Course in Linear Algebra* is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way.

A unique feature of this book is that chapters, sections and theorems are labeled rather than numbered. For example, the chapter on vectors is labeled "Chapter V" and the theorem that elementary matrices are nonsingular is labeled "Theorem EMN."

Another feature of this book is that it is designed to integrateSAGE, an open source alternative to mathematics software such as Matlab and Maple. The author includes a 45-minutevideo tutorialon SAGE and teaching linear algebra.

**For students:**The book comes with supplemental archetypesand printable flashcards.

This textbook has been used in classes at:Centre for Excellence in Basic Sciences, Westmont College, University of Ottawa, Plymouth State University, University of Puget Sound, University of Notre Dame, Carleton University, Amherst College, Felician College, Southern Connecticut State University, Michigan Technological University, Mount Saint Mary College, University of Western Australia, Moorpark College, Pacific University, Colorado State University, Smith College, Wilbur Wright College, Central Washington U (Lynwood Center), St. Cloud State University, Miramar College, Loyola Marymount University.

## About the Contributors

### Author

**Robert A. Beezer** is a Professor of Mathematics at the University of Puget Sound, where he has been on the faculty since 1984. He received a B.S. in Mathematics from the University of Santa Clara in 1978, a M.S. in Statistics from the University of Illinois at Urbana-Champaign in 1982 and a Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign in 1984. He teaches calculus, linear algebra and abstract algebra regularly, while his research interests include the applications of linear algebra to graph theory.