Hermitian matrix vector space over R proof

[Jimena29]

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 a_ij = conjugate(a_ji) 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!

 

[Dick]

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.

 

[Jimena29]

Oh, I thought I also had to prove that the matrix A is contained in R
Thank you very much!