If I have a covariance matrix with rank less than full, I can discard of a variable as long as the remaining variables still span the original space.
But let's say I discover that for $3\times 3$ covariance matrix, I get that $r_1=r_2+r_3$ for a matrix row $r$. Does this mean that $X_1=X_2+X_3$?
*Edit: Maybe I should refine it a bit. My question is about the link from dependency in the covariance matrix, which represents only the 2nd order statistics, and the liner dependency (not statistical dependency) of the variables. Thanks.