span of matrices over finite fields

asked 2018-08-06 11:53:07 +0100

Parker
45 ●2 ●3 ●5

Hello,

I'd to build the span of some matrices defined over GF(4). However, the function span doesn't fit since it seems to interpret matrices as lists of vectors. I tried the following :

F=GF(4);
n=11;
A=random_matrix(F,n);
B=random_matrix(F,n);
print(span(A,F));
print(span([A,B],F));

None of which gives satisfying results (the second one gives an error). So, I wanted to know if there was a way to properly get a span of matrices in sagemath.

Thanks in advance.

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answered 2018-08-06 13:10:54 +0100

tmonteil
27423 ●31 ●204 ●517 http://wiki.sagemath.o...

The issue is that matrices are not considered as vectors, so you can flatten them as vectors first:

sage: S = span([vector(A),vector(B)]) ; S
Vector space of degree 121 and dimension 2 over Finite Field in z2 of size 2^2
Basis matrix:
2 x 121 dense matrix over Finite Field in z2 of size 2^2

Given a vector v in such a space, you can make it a matrix as follows:

sage: v = S.random_element()
sage: matrix(n,n,v)

You can check consistency:

sage: matrix(n,n,vector(A)) == A
True
sage: matrix(n,n,vector(B)) == B
True
sage: v in S
True
sage: vector(A) in S
True

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Asked: 2018-08-06 11:53:07 +0100

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Last updated: Aug 06 '18

span of matrices over finite fields edit

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