CODEWITHSUNDEEP
pythonsage
user46060
user46060

Reputation: 123

Orthogonal Subspaces

I trying to solve the next problem. Let be the chain of subspaces $J1 \subset J2 \subset J3 \subset J4$ over the finite field $\mathbb{F} = GF(3)$, where dimension($J1$) = 2, dimension($J2$) = 4, dim($J3$) = 6 and dim($J4$)=8. I want extract the basis vector of the subspace $J4-J3$, $J3-J2 $ and $J2-J1$. For $J4-J3$ I get, using the next code 

K.<t> = GF(3)
J3vectors = [[1,0,0,0,0,1,0,1],[0,1,0,0,0,1,0,0],[0,0,1,0,0,2,0,2],    [0,0,0,1,0,0,0,2],[0,0,0,0,1,1,0,1],[0,0,0,0,0,0,1,1]]
J3 = span(K,J3vectors) #obviously $J3 \subset J4 = \mathbb{F}^8$
transpose(J3.basis_matrix()).kernel()

But I don't know How I will be able to obtain J3-J2 and J2-J1.

Upvotes: 2

Views: 721

Answers (1)

kcrisman
kcrisman

Reputation: 4402

Is the orthogonal complement functionality useful for you here? (Note the note about finite fields.) Otherwise your approach seems reasonable, actually.

Upvotes: 1

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