1. The problem statement, all variables and given/known data Prove that the eigenvalues of a Hermitian matrix is real. http://www.proofwiki.org/wiki/Hermitian_Matrix_has_Real_Eigenvalues The website says that "By Product with Conjugate Transpose Matrix is Hermitian, v*v is Hermitian. " where v* is the conjugate transpose of v. 2. Relevant equations 3. The attempt at a solution I'm not sure why that is true. v*Av is equal to v*v, and v*Av is a Hermitian matrix. Intuitively, v*v seems like a Hermitian matrix, but I need a real theorem that would show that.