A limit with matrices
Posted: Wed Mar 01, 2017 3:30 pm
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.
$$\lim_{n \rightarrow +\infty} \sum_{k=0}^{n} \frac{B^k}{k!} = A$$
where $B^0$ is to be taken as $B^0 = \mathbb{I}_{n \times n}$ that is the identity $n \times n$ matrix.