Dashboard

Now you are in the subtree of Container for Linear Algebra project. 

Hermitian matrices have real eigenvalues.

Created over 8 years ago, updated 10 days ago

Theorem: Hermitian matrices have real eigenvalues. Proof: If $Av = \lambda v$ with $v \neq 0$, then $v^*Av = \lambda v^*v$ and also $v^*Av = v^*A^*v = (Av)^*v = \overline{\lambda}v^*v$. So $\lambda = \overline{\lambda}$, meaning $\lambda$ is real.