A First Course in Linear Algebra

(6 reviews)


Robert Beezer, University of Puget Sound

Pub Date: 2008

ISBN 13:

Publisher: University of Puget Sound

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Reviewed by Barry Minemyer, Ross Visiting Assistant Professor, The Ohio State University, on 6/11/2015.

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 … read more



Reviewed by James Fowler, Assistant Professor, The Ohio State University, on 6/11/2015.

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 … read more



Reviewed by Christopher Phan, Assistant Professor, Winona State University, on 8/22/2016.

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



Reviewed by Angela Martinek, Instructor, Lane Community College, on 8/22/2016.

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 … read more



Reviewed by Michael Kirby, Professor, Colorado State University, on 12/6/2016.

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 … read more



Reviewed by Richard Hammack, Professor, Virginia Commonwealth University, on 2/9/2017.

I examined this book carefully last semester while searching for a good inexpensive (or free) textbook to adopt for a sophomore-level linear algebra … 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 integrate SAGE, an open source alternative to mathematics software such as Matlab and Maple. The author includes a 45-minute video tutorial on SAGE and teaching linear algebra. 

For students: The book comes with supplemental archetypes and 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.