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