Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose we have hermitian matrix $H$, matrix $A$, composed of eigenvectors of $H$, such that $\langle A\mathbf i\mid A\mathbf i\rangle=1$, where $\mathbf i$ is the $i$-th column of matrix $H$.

  1. How to prove that $A$ is unitary?
  2. $H=ABA'$ ($A'$ is conjugate transpose matrix, $B$ is diagonal matrix, diagonal elements are eigenvalues of $H$)?
  3. $H^n=AB^nA'$?
  4. $B=A'HA$

Thanks much for any help!

share|improve this question
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.