Why is $\mathbb{H} \otimes \mathbb{C} \cong \text{End}_{\mathbb{C}} (\mathbb{H})$

Question

As the title insinuates, in my readings I can across this isomorphism $\mathbb{H} \otimes \mathbb{C} \cong \text{End}_{\mathbb{C}} (\mathbb{H})$ and i cannot see why this is the case. Can someone help me see why this is an isomorphism. Here $\mathbb{H}$ is referring to the quaternions.

Answer 1

You should clarify certain what field you are tensoring over and how you view the quaternions as a complex vector space (left or right: they are not in the center of the quaternions). See Example 2.6 and Exercise 5 of Section 2 here for a starting point.