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%TCIDATA{<META NAME="Title" CONTENT="Matrix Algebra">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 17:16:25 1997}
%TCIDATA{Language=American English}
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%TCIDATA{<LINK REL="contents" HREF="DM0-0.tex">}
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\begin{document}


\section{Matrix Algebra}

\subsubsection{\protect\smallskip Working With Matrices}

\hyperref{+ Introduction}{}{}{DM8-1.tex#Matrix Algebra}

\hyperref{+ Creating Matrices}{}{}{DM8-1.tex#Creating Matrices}

\hyperref{+ Revising Matrices}{}{}{DM8-1.tex#Revising Matrices}

\hyperref{+ Concatenating Matrices}{}{}{DM8-1.tex#Concatenate}

\hyperref{+ Reshaping Lists and Matrices}{}{}{DM8-1.tex#Reshaping}

\subsubsection{Standard Operations}

\hyperref{+ Matrix Addition and Scalar Multiplication}{}{}{%
DM8-2.tex#Standard matrix operations}

\hyperref{+ Inner Products and Matrix Multiplication}{}{}{DM8-2.tex#Matrix
product}

\hyperref{+ Identity and Inverse Matrices}{}{}{DM8-2.tex#Identity matrix}

\hyperref{+ Polynomials with Matrix Values}{}{}{DM8-2.tex#Matrix Values}

\hyperref{+ Operations on Matrix Entries}{}{}{DM8-2.tex#Matrix Entries}

\subsubsection{Row Operations and Echelon Forms}

\hyperref{+ Gaussian Elimination and Row Echelon Form}{}{}{%
DM8-3.tex#Matrices, row operations}

\hyperref{+ Elementary Row Operations}{}{}{DM8-3.tex#Matrices, elementary
row operations}

\subsubsection{Equations}

\hyperref{+ Systems of Linear Equations}{}{}{DM8-4.tex#Systems of equations}

\hyperref{+ Matrix Equations}{}{}{DM8-4.tex#Matrix equations}

\subsubsection{Matrix Operators}

\hyperref{+ Trace}{}{}{DM8-5.tex#Trace}

\hyperref{+ Transpose}{}{}{DM8-5.tex#Transpose}

\hyperref{+ Hermitian Transpose}{}{}{DM8-5.tex#Transpose, Hermitian}

\hyperref{+ Determinant}{}{}{DM8-5.tex#Determinant}

\hyperref{+ Adjugate}{}{}{DM8-5.tex#Adjugate}

\hyperref{+ Permanent}{}{}{DM8-5.tex#Permanent}

\hyperref{+ Maximum and Minimum}{}{}{DM8-5.tex#Maximum and minimum entries}

\hyperref{+ Norm}{}{}{DM8-5.tex#Norm}

\hyperref{+ Condition Number}{}{}{DM8-5.tex#Condition number}

\hyperref{+ Exponential Functions}{}{}{DM8-5.tex#Exponential function,
matrices}

\subsubsection{Polynomials and Vectors Associated with a Matrix}

\hyperref{+ Characteristic Polynomial and Minimum Polynomial}{}{}{%
DM8-6.tex#Characteristic, polynomial}

\hyperref{+ Eigenvalues and Eigenvectors}{}{}{DM8-6.tex#Eigenvectors}

\hyperref{+ Positive Definite Symmetric Matrices}{}{}{DM8-6.tex#Matrices,
positive definite}

\subsubsection{Vector Spaces Associated with a Matrix}

\hyperref{+ Row Space}{}{}{DM8-7.tex#Row space}

\hyperref{+ Column Space}{}{}{DM8-7.tex#Column space}

\hyperref{+ The Left and Right Nullspaces}{}{}{DM8-7.tex#Nullspaces}

\hyperref{+ The QR Factorization and Orthonormal Bases}{}{}{DM8-7.tex#QR
factorization}

\hyperref{+ Rank and Dimension}{}{}{DM8-7.tex#Matrices, rank}

\subsubsection{Special Forms of Matrices}

\hyperref{+ Smith Normal Form}{}{}{DM8-8.tex#Smith normal form}

\hyperref{+ Rational Canonical Form}{}{}{DM8-8.tex#Companion matrix}

\hyperref{+ Jordan Form}{}{}{DM8-8.tex#Jordan form}

\hyperref{+ Orthogonal Matrices}{}{}{DM8-8.tex#Orthogonal matrix}

\hyperref{+ Singular Value Decomposition (SVD)}{}{}{DM8-8.tex#SVD}

\subsubsection{Sample Problems}

\hyperref{+ Exercises}{}{}{DM8-9.tex#Exercises}

\hyperref{+ Solutions}{}{}{DM8-9.tex#Solutions}

\end{document}
