I have no clue how to approach this problem, I've asked for some help from different people, but I have yet to comprehend it. The question is the following,
Let $\mathcal L$($\mathbb C$$^n$) denote the vector space of linear transformation on $\mathbb C$$^n$. Let Laut($\mathbb C^n)$ denote the subset of linear automorphisms of $\mathbb C^n$. Define the mapping,
inv: Laut( $\mathbb C^n$) $\rightarrow$ Laut($\mathbb C^n$): A $\mapsto$ A$^{-1}$.
Find the derivative of inv.
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1$\begingroup$ math.stackexchange.com/questions/190424/… Check out this thread $\endgroup$– JHallidayMay 2, 2015 at 1:08
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$\begingroup$ Can I use this, if $X$ is a normed vector space, $S$ in an open subset of $X$, $f:S\mapsto X$ is differentiable at $x \in S$ if there is an operator $A \in {\mathcal L}(X)$ such that $||f(x+h) - f(x) - Ah|| = o(||h||)$ as $h \mapsto 0$. $\endgroup$– jc_flysMay 2, 2015 at 2:19
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