Proving W is a subspace.

  • Thread starter dylanhouse
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  • #1
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Homework Statement



Given W={A belonging to M2(ℂ) | A is symmetric} is a subspace of M2(ℂ) over ℂ, when showing it is closed under scalar multiplication, do I need to use a complex scalar as it is over the complex numbers, or will a real number be okay?

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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You have to prove that it's closed under scalar multiplication using complex numbers, as the vector space [itex]M_2(\mathbb{C})[/itex] is a vector space over the complex numbers.
 

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