1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proving that the eigenvalues of a Hermitian matrix is real

  1. Dec 7, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove that the eigenvalues of a Hermitian matrix is real.

    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.
  2. jcsd
  3. Dec 7, 2012 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Do you really need a proof that v*v is Hermitian? Some things are just obvious. This is one of those things.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook