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.
Asked
Active
Viewed 62 times
2
jc_flys
- 33
-
1http://math.stackexchange.com/questions/190424/how-to-evaluate-the-derivatives-of-matrix-inverse Check out this thread – JHalliday May 02 '15 at 01:08
-
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 $h \mapsto 0$. – jc_flys May 02 '15 at 02:19