${\displaystyle {}v,w\in V}$

${\displaystyle {}d{\left(v,w\right)}:=\Vert {v-w}\Vert$ :={\sqrt {\left\langle v-w,v-w\right\rangle }}\,}

den Abstand zwischen ${\displaystyle {}v}$ und ${\displaystyle {}w}$.

${\displaystyle {}(M,d)}$

${\displaystyle {}T\subseteq M}$

${\displaystyle {}a\in M}$

${\displaystyle {}T}$

${\displaystyle {}\epsilon >0}$

${\displaystyle {}T\cap U{\left(a,\epsilon \right)}\neq \emptyset \,.}$

${\displaystyle v'=Mv+z,}$

wobei

${\displaystyle M={\begin{pmatrix}a_{11}&a_{12}&\ldots &a_{1n}\\a_{21}&a_{22}&\ldots &a_{2n}\\\vdots &\vdots &\ddots &\vdots \\a_{n1}&a_{n2}&\ldots &a_{nn}\end{pmatrix}}}$

eine Matrix mit Einträgen ${\displaystyle {}a_{ij}\in \mathbb {C} }$ ist und

${\displaystyle z\colon I\longrightarrow \mathbb {C} ^{n}}$

${\displaystyle {}K}$

${\displaystyle {}V}$

${\displaystyle {}K}$

${\displaystyle {}\left\langle -,-\right\rangle }$

${\displaystyle {}V}$

${\displaystyle {}\left\langle v,w\right\rangle =\left\langle w,v\right\rangle \,}$

für alle ${\displaystyle {}v,w\in V}$ gilt.

${\displaystyle {}f}$

${\displaystyle {}P}$

${\displaystyle {}v}$

${\displaystyle \operatorname {lim} _{s\rightarrow 0,s\neq 0}\,{\frac {f(P+sv)-f(P)}{s}},}$

falls dieser existiert.

${\displaystyle {}D_{i}}$

${\displaystyle {}i}$

${\displaystyle {}P\in \mathbb {R} ^{n}}$

${\displaystyle {\begin{pmatrix}D_{1}D_{1}f(P)&\cdots &D_{1}D_{n}f(P)\\\vdots &\ddots &\vdots \\D_{n}D_{1}f(P)&\cdots &D_{n}D_{n}f(P)\end{pmatrix}}}$

die Hesse-Matrix zu ${\displaystyle {}f}$ im Punkt ${\displaystyle {}P}$.

${\displaystyle {}{\frac {\partial G_{i}}{\partial x_{j}}}(P)={\frac {\partial G_{j}}{\partial x_{i}}}(P)\,}$

für alle ${\displaystyle {}P\in U}$ und alle ${\displaystyle {}i,j}$ gilt.