Please, can you give me some hints about this?(adsbygoogle = window.adsbygoogle || []).push({});

Here is a proof of the inverse function theorem.

1. After the statement and proof of a previous lemma, the author puts (L o f) as a composite function. I don't understand this because L is a matrix (the jacobian matrix of f(a) ) and I have not seen in my book (Apostol's) that one can directly consider a matrix as a function that may be articulated with other function to build a composite one.

2. In the proof of Claim 1 the author puts this (j and i are subindexes):

l Dj gi (x) l = l Dj fi (x) - Dj fi (a) l

and I would thank if you can tell me how he introduces the Dj fi (a) there (because, following the definition of function g, I thought that Dj gi (x) = Dj fi (x) ).

Thanks for your good will and your time.

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# Inverse function theorem

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