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## 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.