definitions.tex

\newcommand{\bzero}{\mathbf{0}}
\newcommand{\bone}{\mathbf{1}}

\newcommand{\ba}{\mathbf{a}}
\newcommand{\bA}{\mathbf{A}}

\newcommand{\bb}{\mathbf{b}}
\newcommand{\bB}{\mathbf{B}}

\newcommand{\bc}{\mathbf{c}}
\newcommand{\bC}{\mathbf{C}}

\newcommand{\bd}{\mathbf{d}}
\newcommand{\bD}{\mathbf{D}}

\newcommand{\be}{\mathbf{e}}
\newcommand{\bE}{\mathbf{E}}


\newcommand{\bh}{\mathbf{h}}
\newcommand{\bH}{\mathbf{H}}

\newcommand{\bi}{\mathbf{i}}
\newcommand{\bI}{\mathbf{I}}

\newcommand{\bj}{\mathbf{j}}
\newcommand{\bJ}{\mathbf{J}}

\newcommand{\bk}{\mathbf{k}}
\newcommand{\bK}{\mathbf{K}}

\newcommand{\bl}{\mathbf{l}}
\newcommand{\bL}{\mathbf{L}}

\newcommand{\bm}{\mathbf{m}}
\newcommand{\bM}{\mathbf{M}}

\newcommand{\bq}{\mathbf{q}}
\newcommand{\bQ}{\mathbf{Q}}

\newcommand{\bt}{\mathbf{t}}
\newcommand{\bT}{\mathbf{T}}


\newcommand{\bu}{\mathbf{u}}
\newcommand{\bU}{\mathbf{U}}

\newcommand{\bv}{\mathbf{v}}
\newcommand{\bV}{\mathbf{V}}

\newcommand{\bw}{\mathbf{w}}
\newcommand{\bW}{\mathbf{W}}

\newcommand{\bx}{\mathbf{x}}
\newcommand{\bX}{\mathbf{X}}
\newcommand{\bxt}{\mathbf{x'}}
\newcommand{\bXt}{\mathbf{X'}}

\newcommand{\by}{\mathbf{y}}
\newcommand{\bY}{\mathbf{Y}}


\newcommand{\bz}{\mathbf{z}}
\newcommand{\bZ}{\mathbf{Z}}

\newcommand{\real}{\mathbb{R}}

\newcommand{\hbeta}{\hat \beta}

\newcommand{\xtx}{\mathbf{X'} \mathbf{X}}
\newcommand{\xtxinv}{(\bXt \bX)^{-1}}
\newcommand{\hatmat}{\bX (\bXt \bX)^{-1} \bXt}
\newcommand{\betahat}{(\bXt \bX)^{-1} \bXt \by}
\newcommand{\yhat}{\bX (\bXt \bX)^{-1} \bXt\by}


\newcommand{\beps}{\boldsymbol{\epsilon}}
\newcommand{\bbeta}{\boldsymbol{\beta}}
\newcommand{\bSigma}{\boldsymbol{\Sigma}}
\newcommand{\brho}{\boldsymbol{\rho}}
\newcommand{\bgamma}{\boldsymbol{\gamma}}
\newcommand{\bGamma}{\boldsymbol{\Gamma}}
\newcommand{\bmu}{\boldsymbol{\mu}}

\newcommand{\blambda}{\boldsymbol{\lambda}}

\newcommand{\bdelta}{\boldsymbol{\delta}}

\newcommand{\Var}{\mbox{Var}}
\newcommand{\Cov}{\mbox{Cov}}

\newcommand{\ip}[2]{\langle #1, #2 \rangle}