Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision | |||
frechet_derivative_chain_rule [2013/09/15 20:26] nikolaj |
frechet_derivative_chain_rule [2014/03/21 11:11] (current) |
||
---|---|---|---|
Line 1: | Line 1: | ||
===== Fréchet derivative chain rule ===== | ===== Fréchet derivative chain rule ===== | ||
==== Theorem ==== | ==== Theorem ==== | ||
- | | @#88DDEE: $X,Y,Z$ ... Banach spaces with topology | | + | | @#55CCEE: context | @#55CCEE: $X,Y,Z$ ... Banach spaces with topology | |
- | | @#88DDEE: $f\in C(X,Y)$ | | + | | @#55CCEE: context | @#55CCEE: $f\in C(X,Y)$ | |
- | | @#88DDEE: $g\in C(Y,Z)$ | | + | | @#55CCEE: context | @#55CCEE: $g\in C(Y,Z)$ | |
- | | @#55EE55: $ D(g\circ f)=(Dg)\circ f\ \cdot\ Df $ | | + | | @#55EE55: postulate | @#55EE55: $ D(g\circ f)=(Dg)\circ f\ \cdot\ Df $ | |
where $\circ$ denotes the concatenation of functions of $X,Y$, which is taken to bind stronger than the concatenation $\cdot$ of linear operators. | where $\circ$ denotes the concatenation of functions of $X,Y$, which is taken to bind stronger than the concatenation $\cdot$ of linear operators. | ||
Line 17: | Line 17: | ||
Wikipedia: [[http://en.wikipedia.org/wiki/Chain_rule|Chain rule]], [[http://en.wikipedia.org/wiki/Chain_rule_%28disambiguation%29|Chain rule (disambiguation)]] | Wikipedia: [[http://en.wikipedia.org/wiki/Chain_rule|Chain rule]], [[http://en.wikipedia.org/wiki/Chain_rule_%28disambiguation%29|Chain rule (disambiguation)]] | ||
==== Parents ==== | ==== Parents ==== | ||
- | === Requirements === | + | === Context === |
[[Fréchet derivative]] | [[Fréchet derivative]] |