Let M be an n by m matrix. For a subset S of {1,...,n} let M(S) be the submatrix of M with row indices in S.
I would like to find an S of smallest size such that M(S) has the same number of distinct columns as M. Can anyone suggest a good approach to this problem? Does the problem have a name? Has it been considered somewhere?
Specifically I have a 431 by 2977 matrix M with 270 distinct rows and 2926 distinct columns. I have been able to find 40 rows such that the submatrix with those rows also has 2926 columns. Is there a smaller set of rows?
The matrix can be found at
http://shell.cas.usf.edu/~saito/QuandleColor/rig_1to35_maple_matrix_april7.txt
in case anyone wants to take up the challenge to do better than 40.