Can someone explain what $\operatorname{End}_{\mathbb{C}}(\mathbb{C}[x])$ is? I just want to know what its elements look like.
In the definition, it says that for a field $K$ and $n \in \mathbb{N}$, $M_{n}(K)$ is an algebra over $K.$
I understand what an algebra over $K$ is now.
$M_n(K) = \operatorname{End}_{\mathbb{C}}(\mathbb{C}[x])$ where $M_n(K)$ is the set of all linear transformations from $K^n$ to itself.
Like what is a typical element of $\operatorname{End}_{\mathbb{C}}(\mathbb{C}[x])$? Is it a matrix multiplied by some complex number?