1. ## Linear algebra

Let $H = \begin{bmatrix} u & v \\ -\bar{v} & \bar{u}\end{bmatrix}$ be a subset of 2x2 matrix with entries in complex numbers (vector space V).
1.If V is considered an $\mathbb R$-space, is H a subspace?
My question is not how to find the answer but if being "an $\mathbb R$-space" means that the scalar multiplication is over an $\mathbb R$. Once I know that I should be fine.

2. Originally Posted by vincisonfire
Let $H = \begin{bmatrix} u & v \\ -\bar{v} & \bar{u}\end{bmatrix}$ be a subset of 2x2 matrix with entries in complex numbers (vector space V).
1.If V is considered an $\mathbb R$-space, is H a subspace?
My question is not how to find the answer but if being "an $\mathbb R$-space" means that the scalar multiplication is over an $\mathbb R$. Once I know that I should be fine.
Let $\mathcal{H}$ be a set of all there types of matrices, $H$.
They want you to prove that $\mathcal{H}$ is a vector space over $\mathbb{R}$.
Here vector addition is regular matrix addition and scalar multiplication is scalar matrix multiplication.