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linear-algebra.tex
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linear-algebra.tex
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\documentclass[letterpaper,oneside]{book}%
\newif\ifinstructor
%% uncomment one of the following, depending if you want to include the
%% instructor notes or not
\instructortrue
\instructorfalse
\renewcommand{\thefootnote}{\roman{footnote}}
\newcommand{\note}[1]{\footnote{#1}\marginpar{\fbox{\textbf{\thefootnote}}}}
%%%%%%%To make all notes ignored, uncomment the following command.
\renewcommand{\note}[1]{}
\usepackage[left=1in,right=2.75in,top=1in,bottom=1in]{geometry}
\marginparwidth 1.75in
\usepackage{tabls}
\usepackage{booktabs}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{pstricks}
\usepackage{multicol}
\usepackage{enumitem}
\usepackage{microtype}
\usepackage{makeidx}
\usepackage{index}
\usepackage{etex}
\usepackage{endnotes}
\usepackage{tikz}
\usetikzlibrary{positioning,matrix,arrows,calc}
\tikzset{every picture/.style={>=latex,thick}}
\tikzset{grid lines/.style={semithick,dotted}}
\usepackage{pgfplots}
\pgfplotsset{compat=1.3}
\usepgfplotslibrary{external}
%\tikzexternalize
\tikzsetexternalprefix{figures/}
\newcommand{\remake}{\tikzset{external/force remake}}
\newcommand\marginpartop[1]{\leavevmode\marginpar{#1}}
\newcommand{\aligntop}[1]{\vtop{\vskip-1ex\hbox{ #1}}}
% \newcommand{\marginpartop}[1]{\marginpar{\vtop{%
% \vskip0pt
% \hbox{%
% #1%
% }%
% }}}
\newcommand{\myscale}{1}
\usepackage{graphicx}
\usepackage{wrapfig}
\newcommand{\ds}{\displaystyle}
\newcommand{\dfdx}[1]{\frac{d#1}{dx}}
\newcommand{\ddx}{\frac{d}{dx}}
\let\oldmarginpar\marginpar
\renewcommand\marginpar[1]{\-\oldmarginpar{\raggedright\footnotesize #1}}
%\renewcommand\marginpar[1]{\-\oldmarginpar[\raggedleft\footnotesize #1]{\raggedright\footnotesize #1}}
%\usepackage[12hr]{datetime}
%\newdateformat{draftdate}{%
%\shortdayofweekname{\THEDAY}{\THEMONTH}{\THEYEAR}, %
%\THEDAY\ \shortmonthname[\THEMONTH] \THEYEAR}
%\draftdate
%\usepackage{eso-pic}
%\AddToShipoutPicture{\put(10,10){\small Draft: \today\ at \currenttime }}%--- version: \MakeUppercase{\svnInfoRevision}}}
\theoremstyle{definition}
\newtheorem{theorem}{Theorem}[chapter]
\newtheorem*{theorem*}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem*{lemma*}{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{problem}[theorem]{Problem}
\newtheoremstyle{box}%
{}{}% standard spacing before and after
{}% Body style
{}{\bfseries}{.}% Heading indent, font, and punctuation
{ }% space after heading
{\thmname{#1}\thmnumber{ #2}\thmnote{: #3}}% head spec
\theoremstyle{box}
\newtheorem{definition}{Definition}[chapter]
\newtheorem*{definition*}{Definition}
\newtheorem{observation}[theorem]{Observation}
\newtheorem{remark}{Remark}[chapter]
\newtheorem{example}{Example}[chapter]
\newtheorem{question}{Question}[chapter]
\newtheorem*{prep-problems}{Preparation Problems}
\usepackage{xifthen}% provides \isempty test
\newcommand{\definestyle}[1]{\textit{#1}}
\newcommand{\define}[2][]{\definestyle{#2}\ifthenelse{\isempty{#1}}{\index{#2}}{\index{#1}}}
\newcommand{\definemargin}[2][]{\marginpar{#2}\define[#1]{#2}}
%% seealso command from TUGboat, Volume 12 (1991), No. 2
\def\subsee#1#2{{\em see also\/} #1}
% the #2 consumes a comma
\def\nosee#1{}
% consume the page number
\def\seealso#1#2{%
\index{#1!zzzzz@\subsee{#2}|nosee}}
%% to use, do something like \seealso{index entry}{see also entry}
% Abbreviations
\newcommand{\ii}{\ensuremath{\mathbf{\hat \i}}}
\newcommand{\jj}{\ensuremath{\mathbf{\hat \j}}}
\newcommand{\kk}{\ensuremath{\mathbf{\hat k}}}
\newcommand{\vv}{\ensuremath{\mathbf{v}}}
\newcommand{\colvec}[1]{\ensuremath{\begin{bmatrix}#1\end{bmatrix}}}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\rref}{rref}
\DeclareMathOperator{\vspan}{span}
\DeclareMathOperator{\trace}{tr}
\DeclareMathOperator{\col}{col}
\DeclareMathOperator{\row}{row}
\DeclareMathOperator{\nullspace}{null}
\DeclareMathOperator{\adjugate}{adj} % adjoint
\DeclareMathOperator{\diag}{diag}
\newcommand{\RR}{\ensuremath{\mathbb{R}}}
%The purpose of this code is to allow me to put lines in matrices so that I can create augmented matrices.
\makeatletter
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
\hskip -\arraycolsep
\let\@ifnextchar\new@ifnextchar
\array{#1}}
\makeatother
\newcommand{\cl}[1]{ \begin{matrix} #1 \end{matrix} }
\newcommand{\bm}[1]{ \begin{bmatrix} #1 \end{bmatrix} }
\newcommand{\inv}{^{-1}}
\newcommand{\im}{\ensuremath{\text{im }}}
\newcommand{\R}{\mathbb{R}}
% double-vertical bars for norm
\providecommand{\normd}[1]{\lVert#1\rVert}
% single-vertical bars for norm
\providecommand{\norm}[1]{\left|#1\right|}
% a "such that" symbol for set-builder notation
\newcommand{\st}{\ensuremath{\mid}}
%------------------------------------------------------------------------------------------------------------
\usepackage[pdfpagelabels]{hyperref}
\makeindex
\begin{document}
\frontmatter
\title{Linear Algebra}
\author{Ben Woodruff\\Revised by Jason Grout}
\date{Typeset on \today\\
\vfill
\includegraphics[height=1.3cm]{by-sa}
\vfill}
\maketitle
\copyright{This work is licensed under the Creative Commons
Attribution-Share Alike 3.0 United States License. You may copy,
distribute, display, and perform this copyrighted work but only if
you give credit to Ben Woodruff and all derivative works based
upon it must be published under the Creative Commons
Attribution-Share Alike 3.0 United States License. Please attribute
to Ben Woodruff, Mathematics Faculty at Brigham Young University -
Idaho, [email protected]. To view a copy of this license, visit\\
\centerline{\url{http://creativecommons.org/licenses/by-sa/3.0/us/}}
\\ or send a letter to Creative Commons, 171 Second Street, Suite
300, San Francisco, California, 94105, USA.
\vfill
See \url{https://github.com/jasongrout/linear-algebra} for the source for the book.
}
\tableofcontents
%\chapter*{Preface}
%
%I would like to thank BYU-Idaho for the resources they have provided me to create this text.
%\chapter{Introduction}
%
%The introduction is entered using the usual chapter command. Since
%the introduction chapter appears before the \verb|mainmatter| TeX
%field, it is again an unnumbered chapter. The primary difference
%between the preface and the introduction in this sample document
%is that the introduction will appear in the table of contents and
%the page headings for the introduction are automatically handled
%without the need for the \verb|markboth| TeX field. You may use
%either or both methods to create chapters at the beginning of your
%document. You may also delete these preliminary chapters.
\mainmatter
\include{01-Arithmetic/Arithmetic-Content}
\newgeometry{left=1in,right=1in,top=1in,bottom=1in}
\include{01-Arithmetic/Arithmetic-Problems}
\restoregeometry
\ifinstructor
\include{01-Arithmetic/Arithmetic-Instructor}
\fi
\include{02-Applications/Linear-Algebra-Applications-Content}
\newgeometry{left=1in,right=1in,top=1in,bottom=1in}
\include{02-Applications/Linear-Algebra-Applications-Problems}
\restoregeometry
\ifinstructor
\include{02-Applications/Linear-Algebra-Applications-Instructor}
\fi
\include{03-Patterns/Patterns-Content}
\newgeometry{left=1in,right=1in,top=1in,bottom=1in}
\include{03-Patterns/Patterns-problems}
\restoregeometry
\ifinstructor
\include{03-Patterns/Patterns-Instructor}
\fi
\include{04-Inner-Products/Inner-Products-Content}
\newgeometry{left=1in,right=1in,top=1in,bottom=1in}
\include{04-Inner-Products/Inner-Products-Problems}
\restoregeometry
\include{05-Linear-Transformations/Linear-Transformations-Content}
\newgeometry{left=1in,right=1in,top=1in,bottom=1in}
\include{05-Linear-Transformations/Linear-Transformations-Problems}
\restoregeometry
\ifinstructor
\include{05-Linear-Transformations/Linear-Transformations-Instructor}
\fi
\include{06-Changing-Bases/Changing-Bases-Content}
\theendnotes
\setcounter{endnote}{0}
\newgeometry{left=1in,right=1in,top=1in,bottom=1in}
\include{06-Changing-Bases/Changing-Bases-Problems}
\restoregeometry
%\include{07-Jordan-Form/Jordan-Form-Content}
%\newgeometry{left=1in,right=1in,top=1in,bottom=1in}
%\include{07-Jordan-Form/Jordan-Form-Problems}
%\restoregeometry
%% These are not written yet:
%\include{08-Symmetric-Matrices/Symmetric-Matrices}
%\newgeometry{left=1in,right=1in,top=1in,bottom=1in}
%\include{08-Symmetric-Matrices/Symmetric-Matrices-Problems}
%\restoregeometry
%\include{09-Connections/Connections}
%\newgeometry{left=1in,right=1in,top=1in,bottom=1in}
%\include{09-Connections/Connections-Problems}
%\restoregeometry
\backmatter
\printindex
%\appendix
%
%\chapter{The First Appendix}
%
%The \verb"\appendix" command should be used only once. Subsequent appendices can
%be created using the Chapter command.
%
%\chapter{The Second Appendix}
%
%Some text for the second Appendix.
%
%This text is a sample for a short bibliography. You can cite a book by making use of
%the command \verb"\cite{KarelRektorys}": \cite{KarelRektorys}. Papers can be cited
%similarly: \cite{Bertoti97}. If you want multiple citations to appear in a single set
%of square brackets you must type all of the citation keys inside a single citation,
%separating each with a comma. Here is an example: \cite{Bertoti97, Szeidl2001,
%Carlson67}.
%
%\begin{thebibliography}{9}
%\bibitem {KarelRektorys}Rektorys, K., \textit{Variational methods in Mathematics,
%Science and Engineering}, D. Reidel Publishing Company,
%Dordrecht-Hollanf/Boston-U.S.A., 2th edition, 1975
%
%\bibitem {Bertoti97} \textsc{Bert\'{o}ti, E.}:\ \textit{On mixed variational formulation
%of linear elasticity using nonsymmetric stresses and displacements}, International
%Journal for Numerical Methods in Engineering., \textbf{42}, (1997), 561-578.
%
%\bibitem {Szeidl2001} \textsc{Szeidl, G.}:\ \textit{Boundary integral equations for
%plane problems in terms of stress functions of order one}, Journal of Computational and
%Applied Mechanics, \textbf{2}(2), (2001), 237-261.
%
%\bibitem {Carlson67} \textsc{Carlson D. E.}:\ \textit{On G\"{u}nther's stress functions
%for couple stresses}, Quart. Appl. Math., \textbf{25}, (1967), 139-146.
%\end{thebibliography}
%
%\backmatter
%
%\chapter{Afterword}
%
%The back matter often includes one or more of an index, an afterword,
%acknowledgements, a bibliography, a colophon, or any other similar item. In
%the back matter, chapters do not produce a chapter number, but they are
%entered in the table of contents. If you are not using anything in the back
%matter, you can delete the back matter TeX field and everything that follows it.
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End: