**Disclaimer**  

This is not strictly a programming question, but most programmers soon or later have to deal with math (especially algebra), so I think that the answer could turn out to be useful to someone else in the future.

**Now the problem**  

I'm trying to check if m vectors of dimension n are linearly independent. If m == n you can just build a matrix using the vectors and check if the determinant is != 0. But what if m < n?

Any hints?

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See also [this video lecture](http://academicearth.org/lectures/independence-basis-and-dimension).