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Thread: Linear algebra

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