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I am looking for one-dimension subspace $x$ such that for every $v\in$$\langle x\rangle we have v.v=0. I try this: V = VectorSpace(GF(5),2) for i in V.subspaces(1): for x in i: if (x*x==0): print(i)  but I have trouble with it: sage gives me subspace "Vector space of degree 2 and dimension 1 over Finite Field of size 5 Basis matrix: [1 0]" this subspace is not satisfied my condition ### one-dimension One-dimension subspace I am looking for one-dimension subspace x such that for every v\in$$\langle x\rangle$ we have $v.v=0$.

I try this:

V = VectorSpace(GF(5),2)

for i in V.subspaces(1):

for x in i:
if (x*x==0):
print(i)


but I have trouble with it:

sage gives me subspace "Vector space of degree 2 and dimension 1 over Finite Field of size 5 Basis matrix: [1 0]" this subspace is not satisfied my condition