Is there a function that takes a list like


and decide if the vectors (1,0,3) and (0,-3,1) are linearly independent or not?

It would be great if the output is 1 for yes (they are linearly independent) and 0 for no (they are linearly dependent). I aim to select from a list of lists those whose vectors are linearly independent. Maybe I can use Select to do it because if the output is 0 or 1 I can put the result as a criteria in the argument of Select. For example, Let


I want to obtain from S the subset


of its linearly independent lists.

Another way to do that could be by calculating the minors, but I think this would complicate things.

  • $\begingroup$ You've seen NullSpace[], no? $\endgroup$
    – J. M.'s torpor
    Sep 27 '17 at 17:21

I think the simplest approach is to find the MatrixRank of the list:

S = {

MatrixRank[#] == 2& /@ S

{True, False, False, True}

Then, you can use Pick to obtain what you want:

Pick[S, MatrixRank[#] == 2& /@ S]

{{{1, 0, 13}, {2, 12, 1}}, {{1, 0, 0}, {0, 1, 0}}}


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