# Transforming a symmetric matrix into pentadiagonal form

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?

• what happens with 6 by 6 matrix? – Will Jagy Mar 25 at 18:18
• I really don't know. What happens? Anyway, in the problem I am concerned with the matrices are much larger. – Qwertuy Mar 25 at 19:17
• I imagine matrix $Q$ needs to have real coefficients ? – Pohoua Mar 26 at 0:29