If this is better placed in the general analysis forum, please tell me. I'm new here.

Expanding the Subject:

- real square symmetric positive definite.

- real square positive diagonal.

Under what conditions (sufficient nice; necessary excellent) is

also positive definite?

It is easy to show AD has positive eigenvalues, so the "failure" case is when a negative one pops up in

.

I have not been able to get traction on this. All help appreciated.

Background: The need is to explore convergence of a very large, very nonlinear system of differential equations. My best shot at a Lyapunov function has derivative of the form

.

The system is bounded, so if AD is always positive definite, it will converge. Alas, it starts meandering in experiments exactly when AD becomes indefinite. I'm searching for a fix.

Many thanks for your thoughts.