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\documentclass{ximera}
\title{Linear Algebra}
\begin{document}
\begin{abstract}
By using linear algebra, seeming different ``linear'' things in algebra, geometry, and calculus—things like systems of certain equations, rigid motions in geometry, certain differential equations—can be placed in a common framework of vectors, matrices, and linear transformations. Viewing different things as somehow analogous provides not only insight, but also a common toolkit of surprisingly powerful algorithms.
\end{abstract}
\maketitle
\begin{center}
\Huge This is Linear Algebra
\end{center}
Authored by Rob Beezer (the original textbook) and modified by Jim
Fowler for as a demo of Ximera. Published by the MOOCulus team at The
Ohio State University. Copyright 2004--2015, Robert A. Beezer.
Copyright 2016, Jim Fowler.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with no
Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A
copy of the license is included in the section entitled ``GNU Free
Documentation License.''
\section{History}
The original version was created 2004--2015 and is available at
http://linear.ups.edu/ and is authored by Robert A.~Beezer and
published on the web.
This modified version is meant to be a demo of what an ``interactive''
version of the text might look like. Ideally, the underlying
MathBook~XML would export directly to a Ximera-compatible \LaTeX\
format, but since it is not even entirely clear what sorts of
``interactive'' features might be desirable, Fowler has been modifying
the MathBook XML into this demo.
The transparent version of this demo ``interactive'' text is available
at https://github.com/mooculus/linearAlgebra
\section{Dedications}
Robert A. Beezer: ``To my wife, Pat.''
\section{Acknowledgements}
Many people have helped to make this book, and its freedoms, possible.
First, the time to create, edit and distribute the book has been
provided implicitly and explicitly by the University of Puget Sound. A
sabbatical leave Spring 2004, a course release in Spring 2007 and a
Lantz Senior Fellowship for the 2010-11 academic year are three
obvious examples of explicit support. The course release was provided
by support from the Lind-VanEnkevort Fund. The university has also
provided clerical support, computer hardware, network servers and
bandwidth. Thanks to Dean Kris Bartanen and the chairs of the
Mathematics and Computer Science Department, Professors Martin
Jackson, Sigrun Bodine and Bryan Smith, for their support,
encouragement and flexibility.
My colleagues in the Mathematics and Computer Science Department have
graciously taught our introductory linear algebra course using earlier
versions and have provided valuable suggestions that have improved the
book immeasurably. Thanks to Professor Martin Jackson (v0.30),
Professor David Scott (v0.70), Professor Bryan Smith (v0.70, 0.80,
v1.00, v2.00, v2.20), Professor Manley Perkel (v2.10), and Professor
Cynthia Gibson (v2.20).
University of Puget Sound librarians Lori Ricigliano, Elizabeth Knight
and Jeanne Kimura provided valuable advice on production, and
interesting conversations about copyrights.
Many aspects of the book have been influenced by insightful questions
and creative suggestions from the students who have labored through
the book in our courses. For example, the flashcards with theorems and
definitions are a direct result of a student suggestion. I will single
out a handful of students at the University of Puget Sound who have
been especially adept at finding and reporting mathematically
significant typographical errors: Jake Linenthal, Christie Su, Kim Le,
Sarah McQuate, Andy Zimmer, Travis Osborne, Andrew Tapay, Mark
Shoemaker, Tasha Underhill, Tim Zitzer, Elizabeth Million, Steve
Canfield, Jinshil Yi, Cliff Berger, Preston Van Buren, Duncan Bennett,
Dan Messenger, Caden Robinson, Glenna Toomey, Tyler Ueltschi, Kyle
Whitcomb, Anna Dovzhik, Chris Spalding and Jenna Fontaine. All the
students of the Fall 2012 Math 290 sections were very helpful and
patient through the major changes required in making Version 3.00.
I have tried to be as original as possible in the organization and
presentation of this beautiful subject. However, I have been
influenced by many years of teaching from another excellent textbook,
Introduction to Linear Algebra by L.W. Johnson, R.D. Reiss and
J.T. Arnold. When I have needed inspiration for the correct approach
to particularly important proofs, I have learned to eventually consult
two other textbooks. Sheldon Axler's Linear Algebra Done Right is a
highly original exposition, while Ben Noble's Applied Linear Algebra
frequently strikes just the right note between rigor and
intuition. Noble's excellent book is highly recommended, even though
its publication dates to 1969.
Conversion to various electronic formats have greatly depended on
assistance from: Eitan Gurari, author of the powerful LaTeX
translator, tex4ht; Davide Cervone, author of jsMath and MathJax; and
Carl Witty, who advised and tested the Sony Reader format. Thanks to
these individuals for their critical assistance.
Incorporation of Sage code is made possible by the entire community of
Sage developers and users, who create and refine the mathematical
routines, the user interfaces and applications in educational
settings. Technical and logistical aspects of incorporating Sage code
in open textbooks was supported by a grant from the United States
National Science Foundation (DUE-1022574), which has been administered
by the American Institute of Mathematics, and in particular, David
Farmer. The support and assistance of my fellow Principal
Investigators, Jason Grout, Tom Judson, Kiran Kedlaya, Sandra Laursen,
Susan Lynds, and William Stein is especially appreciated.
David Farmer and Sally Koutsoliotas are responsible for the vision and
initial experiments which lead to the knowl-enabled web version, as
part of the Version 3 project.
General support and encouragement of free and affordable textbooks, in
addition to specific promotion of this text, was provided by Nicole
Allen, Textbook Advocate at Student Public Interest Research
Groups. Nicole was an early consumer of this material, back when it
looked more like lecture notes than a textbook.
Finally, in every respect, the production and distribution of this
book has been accomplished with open source software. The range of
individuals and projects is far too great to pretend to list them
all. This project is an attempt to pay it forward.
\end{document}
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