If you have run mixed models much at all, you have undoubtedly been haunted by some version of this very obtuse warning: “The 
Hessian (or G or D) Matrix is not positive definite. Convergence has stopped.”
Or “The Model has not Converged. Parameter Estimates from the last iteration are displayed.”
What on earth does that mean?
Let’s start with some background. If you’ve never taken matrix algebra, (more…)