Let $\displaystyle H = \begin{bmatrix} u & v \\ -\bar{v} & \bar{u}\end{bmatrix} $ be a subset of 2x2 matrix with entries in complex numbers (vector space V).

1.If V is considered an $\displaystyle \mathbb R$-space, is H a subspace?

My question is not how to find the answer but if being "an $\displaystyle \mathbb R$-space" means that the scalar multiplication is over an $\displaystyle \mathbb R$. Once I know that I should be fine.