How can I get n(maybe 10) vectors that are linearly independent from a vector space?
gen=VectorSpace(GF(29),9)
basis=[gen.random_element() for i in range(10)]
print(gen.linear_dependence(basis)==[]) #False
You can get up to 9 linearly independent vectors from a 9-dimensional space. This gives 9 vectors over GF(29), if you need less - just pick a subset of them:
Matrix( SL(9, GF(29)).random_element() ).rows()
Another approach, maybe more along the lines you were thinking:
sage: gen=VectorSpace(GF(29),9)
sage: basis = []
sage: while len(basis) < gen.dimension():
....: v = gen.random_element()
....: if not gen.linear_dependence(basis + [v]):
....: basis.append(v)
....:
Asked: 2022-01-28 21:37:09 +0200
Seen: 364 times
Last updated: Jan 30 '22
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You cannot get 10 linearly independent vectors in a 9-dimensional vector space.