JHi all! Just browsing through some materials on proving efficiency of GLS over OLS, vice versa, and one of the methodology was to compare their respective variances, that for OLS to be more efficient, the difference between both, GLS - OLS variance should be positive semi-definite.
Therefore, when there's an actual numerical or algebraic question, does one look to check if the difference between both variance is greater than 0 ? (to explain if it may be positive definite or positive semi-definite)
How to definite if that (the difference of two variance) is positive definite or positive semi-definite?
Separately there seem to be a vector expression evaluation for potential positive definite / semi-definite which am not sure if may be related...