Read more about A First Course in Linear Algebra

A First Course in Linear Algebra

(11 reviews)

Robert A. Beezer, University of Puget Sound

Copyright Year: 2015

ISBN 13: 9780984417551

Publisher: Independent

Language: English

Read this book

Conditions of Use

Free Documentation License (GNU)
Free Documentation License (GNU)


Learn more about reviews.

Reviewed by Jessica Giglio, Assistant Professor II, Central Oregon Community College on 6/19/19

The course covers all the topics I would expect to see in an introductory linear algebra course, plus more, and at an appropriate depth. However, there are very few figures and little discussion of a geometric perspective (which admittedly the... read more

Reviewed by Teena Carroll, Associate Professor of Mathematics, Emory and Henry College on 3/26/19

The standard set of topics is covered with many additional topics interspersed. Review topics such as proof techniques and properties of complex numbers are included as supplements. There are many nonstandard ways to navigate this book, but a... read more

Reviewed by Jason Gaddis, Assistant Professor, Miami University on 8/2/18

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

Reviewed by Gabriel Tapia, Teaching Instructor, West Virginia University on 6/19/18

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

Reviewed by Emese Kennedy, Visiting Assistant Professor, Hollins University on 5/21/18

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

Reviewed by Richard Hammack, Professor, Virginia Commonwealth University on 2/8/17

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

Reviewed by Michael Kirby, Professor, Colorado State University on 12/5/16

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

Reviewed by Angela Martinek, Instructor, Lane Community College on 8/21/16

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

Reviewed by Christopher Phan, Assistant Professor, Winona State University on 8/21/16

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

Reviewed by Barry Minemyer, Ross Visiting Assistant Professor, The Ohio State University on 6/10/15

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

Reviewed by James Fowler, Assistant Professor, The Ohio State University on 6/10/15

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

  • Systems of Linear Equations
  • Vectors
  • Matrices
  • Vector Spaces
  • Determinants
  • Eigenvalues
  • Linear Transformations
  • Representations
  • Preliminaries
  • Reference

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


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.