Kategorie:Funktionalmatrix

Funktionalmatrix[Bearbeiten | Quelltext bearbeiten]

Definition der Funktionalmatrix einer mehrdimensionalen Funktion ${\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} ^{m}}$, d.h. ${\displaystyle f(x_{1},\ldots ,x_{n})\doteq {\begin{pmatrix}f_{1}(x_{i})\\\vdots \\f_{m}(x_{i})\end{pmatrix}}}$:

${\displaystyle J_{f}={\frac {\partial f}{\partial x}}={\begin{pmatrix}{\frac {\partial f_{1}}{\partial x_{1}}}&{\frac {\partial f_{1}}{\partial x_{2}}}&\ldots &{\frac {\partial f_{1}}{\partial x_{n}}}\\\vdots &\vdots &\ddots &\vdots &\\{\frac {\partial f_{m}}{\partial x_{1}}}&{\frac {\partial f_{m}}{\partial x_{2}}}&\ldots &{\frac {\partial f_{m}}{\partial x_{n}}}\end{pmatrix}}}$