# Vector space whose dimension is nontrivial to determine [closed]

Is there any vector space which is easy to proven to be a vector space but whose dimension is nontrivial to determine?

I want such a case as an exercise for the students.

• te solutions of a linear system $Ax = 0$, where the rank of $A$ is not trivial to determine ? Nov 7 '15 at 10:41
• Solution space of a linear differential equation?
– user99914
Nov 7 '15 at 10:50
• The span, over the rationals, of the zeros of the zeta function in the critical strip but off the half-line. Nov 7 '15 at 11:42
• Not sure why this is getting close votes--the context is quite clear from the final sentence of the question. Nov 10 '15 at 5:33

What qualifies as a non-trivial method to determine the dimension? As @Tlön Uqbar Orbis Tertius mentioned in his comment, this can mean 'not easy to calculate the dimension by hand', in the case of a vector space given by ker($A$), but then the dimension is determined by rank $A$, even if it's hard to compute.