Typical number of rows and columns: I would say the maximum you find in a calculation would be 500, and that would be something like using the S&P 500 to test something, or maybe a CDO. The thing is that for practical situations you usually aren't very sure of the (500 x 500 - 500)/2 pairwise correlations, and wouldn't go out to try and understand them and hedge them all individually.On the other hand, if you are looking at a large "correlation book" in a derivatives group, you could easily have by default a large matrix which contains every underlying for which there is a position. But this will have a sparse block diagonal form corresponding to deals that have actually been done. i would hazard a guess that the big french correlation traders would have a correlation matrix taking in the SBF 120 index.Practicaly speaking for structured products and deal pricing, some of the mountain range bonds had 20-30 stocks.In credit derivatives, the correlation matrix in a normal synthetic CDO would be around 125 x 125.There are many pricing situations though in which you would have 2 or 3 correlated underlyings.

A related question (and probably obivious), is it always the case that:Where A_Cov and A_Corr are the cholesky decomposed covariance and correlation matricies respectively and z is a vector of Normal variates?