Linear algebra

**vincisonfire** · February 4th 2009, 02:02 PM

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.

**ThePerfectHacker** · February 4th 2009, 04:11 PM

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.

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