Roger Hui wrote: > To work with rows rather than columns, transpose > the matrix, and then: > > Method 0: the columns are linearly independent if > the matrix is invertible. > > lii=: 1:@%. ::0: > > Method 1: the columns are linearly independent > if the determinant is non-zero: > > lid=: 0: ~: [: -/ .* (|: +/ .* ])^:(>/@$)
I agree that this is the best way to go with square matrices. The rref method I suggested (which mimics pencil and paper methods) is a good start for nonsquare matrices. It can probably done better than my suggested code. However, the question of finding the rank of a matrix is difficult numerically. The method usually suggested is singular value decomposition, but there has been a lot of work on methods for special matrices. See, for example <http://www.neiu.edu/~zzeng/Papers/rankrev.pdf> Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
