[_a_a_a_]

> You know how someone walking down the street might give you a collection of vectors over a field, and ask questions about the subspace the vectors generate

what on earth...? I can't make sense of the last 2/3ds and with the first 1/3rd it is just weird. What does any of it mean anyway?

[NtochkaNzvanova]

Most of these concepts (except Groebner bases) are basic stuff you would learn in a first course in linear algebra. If you don't know what they mean, this post is likely not relevant to you.

[jjtheblunt]

A simple analogy would be that a groebner basis, for a set of given polynomials, is similar to an orthonormal basis for a set of vectors.

[jjtheblunt]

( Well doesn’t happen quite like that usually, unless the Someone is your math phd research Prof. looking to generalize an idea. )