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Homework Help: Hermitian matrix vector space over R proof!

  1. Feb 11, 2010 #1
    1. The problem statement, all variables and given/known data
    I need to prove that the hermitian matrix is a vector space over R

    2. Relevant equations

    3. The attempt at a solution
    I know the following:
    If a hermitian matrix has aij = conjugate(aji) then its easy to prove that the sum of two hermitian matrices A,B give a hermitian matrix.
    Multiplying a Hermitian matrix by a real number k will also give a hermitian matrix.
    The zero vector is an element of the set of all Hermitian matrices.
    So I can prove that hermitian matrices are a vector space, but what I`m stuck on is how a hermitian matrix is an element of real matrices??
    How are complex numbers elements of R?
    Thank you!
  2. jcsd
  3. Feb 11, 2010 #2


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    Science Advisor
    Homework Helper

    A complex number is not an element of R, nor does a Hermitian matrix necessarily have real elements. You've already proved exactly what you need to prove. The Hermitian matrices are a vector space over R. They wouldn't be a vector space over C.
  4. Feb 11, 2010 #3
    Oh, I thought I also had to prove that the matrix A is contained in R
    Thank you very much!!
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