# Linear algebra

• Feb 4th 2009, 02:02 PM
vincisonfire
Linear algebra
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. (Nod)
• Feb 4th 2009, 04:11 PM
ThePerfectHacker
Quote:

Originally Posted by vincisonfire
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. (Nod)

Let $\displaystyle \mathcal{H}$ be a set of all there types of matrices, $\displaystyle H$.
They want you to prove that $\displaystyle \mathcal{H}$ is a vector space over $\displaystyle \mathbb{R}$.
Here vector addition is regular matrix addition and scalar multiplication is scalar matrix multiplication.