Proving that the eigenvalues of a Hermitian matrix is real

[stgermaine]

Homework Statement

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.

Homework Equations

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.

 

[D H]

Do you really need a proof that v*v is Hermitian? Some things are just obvious. This is one of those things.