Hermitian matrix vector space over R proof!

  • Thread starter Jimena29
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  • #1
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Homework Statement


I need to prove that the hermitian matrix is a vector space over R

Homework Equations





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!
 

Answers and Replies

  • #2
Dick
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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.
 
  • #3
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Oh, I thought I also had to prove that the matrix A is contained in R
Thank you very much!!
 

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