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One-dimension subspace

asked 2013-02-05 03:33:19 +0200

Babgen gravatar image

updated 2013-02-05 07:36:17 +0200

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):

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

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answered 2013-02-05 05:27:55 +0200

ppurka gravatar image

You need to take care of the zero element of the subspace. for x in i will iterate over all the vectors including the zero vector.

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how can I take care of the zero element?

Babgen gravatar imageBabgen ( 2013-02-05 07:34:43 +0200 )edit

If the subspaces are not too big, you can do for x in i[1:]: # rest of your code If the subspaces are big, then doing `i[1:]` will take time and memory. In this case, change your if condition if x != i.zero_vector() and x*x == 0: # rest of your code.

ppurka gravatar imageppurka ( 2013-02-05 09:54:17 +0200 )edit

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Asked: 2013-02-05 03:33:19 +0200

Seen: 268 times

Last updated: Feb 05 '13