1
$\begingroup$

We know any Hermitian matrix is Diagonizable over C always . And If the entries are real then it is a symmetric matrix so it is Diagonizable over R as well as C

So here my Question is.. Does there exist any Hermitian matrix with at least one non real entry such that The matrix is Diagonizable over R

$\endgroup$
1
2
$\begingroup$

If the hermitian matrix $A$ is diagonalizable over the reals, then there are real matrices $D$ (diagonal) and $S$ (invertible) such that $A = SDS^{-1}$. Hence $A$ is a product of real matrices. And $A$ is real.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.