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If n>= (number of rows) then it's quite trivial linear algebra problem.
If n< (number of rows) it is much less trivial and requires formulating a hypothesis about your data. It also depends on the nature of your data, i.e.
can some data, column 4 for instance, be completely uncorrelated with column (n+1).
Check factor analysis for specifics.
http://en.wikipedia.org/wiki/Factor_analysis
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v nice. Thanks.
re bolded part: would that, in the end, matter? Obv it would be best to not have uncorrelated data for sake of computational time, but, I would assume that as long as there is a lot of data, the coefficient on uncorrelated terms --> 0, no?
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Yeah, in principle you'd get 0 for an uncorrelated data, it just can increase the computational cost by a big factor if you try to 'brute force' it.
If I had to solve such a problem I would try to formulate a hypothesis, which would take the physics of the process into account.