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| ===== Fréchet derivative ===== | ===== Fréchet derivative ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $X,Y$ ... Banach spaces with topology | | + | | @#55CCEE: context | @#55CCEE: $X,Y$ ... Banach spaces with topology | |
| - | | @#88DDEE: $\mathcal O$ ... open in $X$ | | + | | @#55CCEE: context | @#55CCEE: $\mathcal O$ ... open in $X$ | |
| - | | @#FFBB00: $D:\mathrm{Continuous}(\mathcal O,Y)\to \mathrm{Continuous}(\mathcal O,\mathrm{BoundedLinOp}(X,Y))$ | | + | | @#FFBB00: definiendum | @#FFBB00: $D:\mathrm{Continuous}(\mathcal O,Y)\to \mathrm{Continuous}(\mathcal O,\mathrm{BoundedLinOp}(X,Y))$ | |
| - | | @#FFBB00: $Df:=x\mapsto J_x^f$ | | + | | @#FFBB00: definiendum | @#FFBB00: $Df:=x\mapsto J_x^f$ | |
| For $J_x f$, see [[Linear approximation]]. | For $J_x f$, see [[Linear approximation]]. | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | This defintion does nothing more than emphasizing the functionality of $L_x^f$ in $f$. | + | This definition does nothing more than emphasizing the functionality of $L_x^f$ in $f$. |
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Derivative_of_a_function|Derivative of a function]], [[http://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative|Fréchet derivative]] | Wikipedia: [[http://en.wikipedia.org/wiki/Derivative_of_a_function|Derivative of a function]], [[http://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative|Fréchet derivative]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Linear approximation]] | [[Linear approximation]] | ||
