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Math Help - Linear algebra

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    Senior Member vincisonfire's Avatar
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    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.
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    Quote Originally Posted by vincisonfire View Post
    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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