%%  File:  linAlgReviewGuide.tex
%%
%%  Study Guide for Numerical Methods with MATLAB
%%  Chapter 7, "A Review of Linear Algebra"
%%
%%  Gerald Recktenwald,  gerry@me.pdx.edu
%%  August 2000


\documentclass{article}

\usepackage{studyGuide}
\renewcommand{\guideName}{Study Guide for Linear Algebra Review}

\title{Study Guide for Linear Algebra Review}
\author{Gerald Recktenwald}

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\begin{document}

%\maketitle

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\section*{Bare Essentials}
At the end of this chapter you should be able to
\begin{enumerate}
    \item   Identify which addition, subtraction, and multiplication operations
            are legal for vectors and matrices.
    \item   Manually carry out legal addition, subtraction,
            and multiplication operations involving vectors and matrices
    \item   Apply transpose operators to vectors and matrices.
    \item   Manually compute each of the vector norms, $L_1$, $L_2$, and $L_\infty$.
    \item   Compute and compare lengths of vectors with the $L_2$ norm.
    \item   Manually compute the inner product of two vectors.
    \item   Use an inner product to verify whether two vectors are orthogonal.
    \item   Use an inner product to verify whether two vectors are orthonormal.
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\end{enumerate}

\bigskip
\noindent To perform basic linear algebra with \MATLAB\ you will need to
\begin{enumerate}
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    \item   Define vector and matrix variables with assignment operations
            \begin{itemize}
                \item   involving \texttt{[ \ldots ]}, and using spaces, commas,
                        and semicolons (as appropriate) to separate row and column
                        elements.
                \item   using built-in functions that return vectors and matrices.
            \end{itemize}
    \item   Extract vector and matrix elements with subscripts.
    \item   Use colon notation to create ranges of subscripts, and thereby extract
            or assign element values \emph{en masse}.
    \item   Use \MATLAB\ syntax to add, subtract, and multiply vectors and matrices.
    \item   Use the $L_2$ norm to write a \MATLAB\ expression to test whether two
            vectors are ``equal to within a tolerance''.
\end{enumerate}


% -------------------------
\section*{An Expanded Core of Knowledge}
After mastering the bare essentials you should move on to a deeper understanding
of the fundamentals.  Doing so involves being able to
\begin{enumerate}
    \item   Use row- and column-oriented algorithms for matrix--vector, vector--matrix,
            and matrix--matrix multiplication.
    \item   Express conditions of linear dependence of vectors (row or column) in terms of
            matrix rank.
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\end{enumerate}

\bigskip
\noindent To perform more advanced linear algebra operations with \MATLAB\ you will need to
\begin{enumerate}
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    \item   Express products of matrices with vectors and other matrices using
            colon notation to make the row and column operations explicit.
\end{enumerate}

% -------------------------
\section*{Developing Mastery}
Working toward mastery of linear algebra you will need to
\begin{enumerate}
    \item   Integrate the linear algebra operations from Chapter~7 with the
            material from Chapter~8 and Chapter~9.  In particular, be able to
            express row-wise operations in Gaussian elimination using colon notation.
\end{enumerate}


\end{document}