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!