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 Post subject: A limit with matricesPosted: Wed Mar 01, 2017 3:30 pm

Joined: Sat Nov 14, 2015 6:32 am
Posts: 146
Location: Melbourne, Australia
Let $A$ be an $n \times n$ invertible real matrix. Show that there is a complex matrix $B$ such that

$$\lim_{n \rightarrow +\infty} \sum_{k=0}^{n} \frac{B^k}{k!} = A$$

where $B^0$ is to be taken as $B^0 = \mathbb{I}_{n \times n}$ that is the identity $n \times n$ matrix.

_________________
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$

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