# Hermitian matrix vector space over R proof!

1. Feb 11, 2010

### Jimena29

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. Feb 11, 2010

### 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.

3. Feb 11, 2010

### Jimena29

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