z_math_commands.tex

% This file contains all of the mathematical commands used in the book

\renewcommand*{\pd}[3][]{\ensuremath{\frac{\partial^{#1} #2}{\partial #3}}}

\newcommand{\mA}{\mathbf{A}}
\newcommand{\mB}{\mathbf{B}}
\newcommand{\mC}{\mathbf{C}}
\newcommand{\mD}{\mathbf{D}}
\newcommand{\mE}{\mathbf{E}}
\newcommand{\mF}{\mathbf{F}}
\newcommand{\mH}{\mathbf{H}}
\newcommand{\mI}{\mathbf{I}}
\newcommand{\mJ}{\mathbf{J}}
\newcommand{\mL}{\mathbf{L}}
\newcommand{\mM}{\mathbf{M}}
\newcommand{\mP}{\mathbf{P}}
\newcommand{\mQ}{\mathbf{Q}}
\newcommand{\mR}{\mathbf{R}}
\newcommand{\mS}{\mathbf{S}}
\newcommand{\mU}{\mathbf{U}}
\newcommand{\mV}{\mathbf{V}}
\newcommand{\mX}{\mathbf{X}}
\newcommand{\mY}{\mathbf{Y}}

\newcommand{\mAi}{\mathbf{A}^{-1}}
\newcommand{\mBi}{\mathbf{B}^{-1}}
\newcommand{\mCi}{\mathbf{C}^{-1}}
\newcommand{\mPi}{\mathbf{P}^{-1}}
\newcommand{\mRi}{\mathbf{R}^{-1}}
\newcommand{\mXi}{\mathbf{X}^{-1}}
\newcommand{\mYi}{\mathbf{Y}^{-1}}

\newcommand{\mXp}{\mathbf{X}^{+}}


%%%%% TRANSPOSES
\newcommand{\T}{^\mathsf{T}}
\newcommand{\mAT}{\mathbf{A}^{\mathsf{T}}}
\newcommand{\mBT}{\mathbf{A}^{\mathsf{T}}}
\newcommand{\mCT}{\mathbf{A}^{\mathsf{T}}}
\newcommand{\mDT}{\mathbf{A}^{\mathsf{T}}}
\newcommand{\mET}{\mathbf{A}^{\mathsf{T}}}
\newcommand{\mXT}{\mathbf{X}^{\mathsf{T}}}

\newcommand{\mXiT}{\mathbf{X}^{-\mathsf{T}}}

\newcommand{\va}{\mathbf{a}}
\newcommand{\vb}{\mathbf{b}}
\newcommand{\vc}{\mathbf{c}}
\newcommand{\vd}{\mathbf{d}}
\newcommand{\ve}{\mathbf{e}}
\newcommand{\vf}{\mathbf{f}}
\newcommand{\vg}{\mathbf{g}}
\newcommand{\vp}{\mathbf{p}}
\newcommand{\vq}{\mathbf{q}}
\newcommand{\vu}{\mathbf{u}}
\newcommand{\vv}{\mathbf{v}}
\newcommand{\vw}{\mathbf{w}}
\newcommand{\vx}{\mathbf{x}}
\newcommand{\vy}{\mathbf{y}}
\newcommand{\vz}{\mathbf{z}}

\newcommand{\vaT}{\mathbf{a}^\mathsf{T}}
\newcommand{\vbT}{\mathbf{b}^\mathsf{T}}
\newcommand{\vuT}{\mathbf{u}^\mathsf{T}}
\newcommand{\vvT}{\mathbf{v}^\mathsf{T}}
\newcommand{\vxT}{\mathbf{x}^\mathsf{T}}

\newcommand{\vzero}{\mathbf{0}}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\eig}{eig}
\DeclareMathOperator{\trace}{tr}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\nnz}{nnz}
\newcommand{\sPSD}{\mathbb{S}^n_+}
\newcommand{\sC}{\mathbb{C}}
\newcommand{\sCmn}{\mathbb{C}^{m,n}}
\newcommand{\sCnn}{\mathbb{C}^{n,n}}
\newcommand{\sR}{\mathbb{R}}
\newcommand{\sRm}{\mathbb{R}^{m}}
\newcommand{\sRn}{\mathbb{R}^{n}}
\newcommand{\sRp}{\mathbb{R}^{p}}
\newcommand{\sRkk}{\mathbb{R}^{k,k}}
\newcommand{\sRkn}{\mathbb{R}^{k,n}}
\newcommand{\sRnm}{\mathbb{R}^{n,m}}
\newcommand{\sRmn}{\mathbb{R}^{m,n}}
\newcommand{\sRnn}{\mathbb{R}^{n,n}}
\newcommand{\sRnk}{\mathbb{R}^{n,k}}
\newcommand{\sRnp}{\mathbb{R}^{n,p}}
\newcommand{\sRnr}{\mathbb{R}^{n,r}}
\newcommand{\sRmm}{\mathbb{R}^{m,m}}
\newcommand{\sSn}{\mathbb{S}^{n}}
\newcommand{\ispsd}{\succeq}
\newcommand{\ispd}{\succ}
\newcommand{\pinv}{\!^+}
\newcommand{\ns}{\mathcal{N}}
\newcommand{\range}{\mathcal{R}}
\newcommand{\bs}{\setminus}
\newcommand{\kp}{\otimes}       %Kronecker product
\newcommand{\hp}{\circ}         %Hadamard product
\newcommand{\grad}{\nabla}      %Gradient operator