Given a symmetric matrix $A$, which has complex values in the diagonal, but whose all other entries are real, I am interested in finding an orthonormal transformation $Q$ such that $Q^tAQ$ is a pentadiagonal matrix whose entries outside of the main diagonal are real. So far, I have not even been able to prove if it's possible to always find such a transformation. Is there maybe any constructive numerical algortihm to attain this?
$\begingroup$
$\endgroup$
3
-
$\begingroup$ what happens with 6 by 6 matrix? $\endgroup$– Will JagyCommented Mar 25, 2021 at 18:18
-
$\begingroup$ I really don't know. What happens? Anyway, in the problem I am concerned with the matrices are much larger. $\endgroup$– QwertuyCommented Mar 25, 2021 at 19:17
-
$\begingroup$ I imagine matrix $Q$ needs to have real coefficients ? $\endgroup$– PohouaCommented Mar 26, 2021 at 0:29
Add a comment
|