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How to find orthogonal subspace of a subspace

asked 2021-10-14 20:52:10 +0100

Sanu gravatar image

I have written a code:

n=4
V = VectorSpace(GF(2),n) C=[[0,0,1,0], [1,1,1,0]]
U = V.subspace(C)

How to find orthogonal subspace of U?

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answered 2021-10-15 13:01:54 +0100

philipp7 gravatar image

You can use the method complement. In your case:

sage: U_perp = U.complement()
sage: U_perp
Vector space of degree 4 and dimension 2 over Finite Field of size 2
Basis matrix:
[1 1 0 0]
[0 0 0 1]

We can easily check that this is indeed the orthogonal complement:

sage: [ b*c for b in U_perp.basis() for c in U.basis() ]
[0, 0, 0, 0]
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Asked: 2021-10-14 20:52:10 +0100

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Last updated: Oct 15