I studied mathematics a decade ago, so I have a math and stats background, but this question is killing me.
This question is still a bit philosophical to me. Why did statisticians develop all sort of techniques in order to work with random matrices? I mean, didn't a random vector solve the problem? If not, what is the mean of the diferent columns of a random matrix? Anderson (2003, Wiley) considers a random vector a special case of a random matrix with only one column.
I don't see the point of having random matrices (and I'm sure that's because I'm ignorant). But, bear with me. Imagine I have a model with 20 random variables. If I want to compute the joint probability function, why should I picture them as a matrix instead of a vector?
What am I missing?
ps: I'm sorry for the poorly tagged question, but there were no tags for random-matrix and I can't create one yet!
edit: changed matrix to matrices in the title