# Checking the existence of linearly dependent vectors from a set of vectors

Assume that we have a set of vectors with cardinality $n$ in a dimension $d$ vector space. I need to check if there exists any number of $d$ vectors in the set which is linearly dependent. Is there any more efficient way than checking the linear dependence of all possible $d$-tuple vectors?

• If you're doing calculations explicitly, it is helpful to note that if you write the $d$ vectors as a $d \times d$ matrix, its determinant is zero if and only if the vectors are linearly dependent. See here for more. – Bill Wallis May 4 '18 at 12:29