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