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Proving W is a subspace.

  1. Sep 19, 2013 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 19, 2013 #2
    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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