vectors, [ambient_space=None]) |
INPUT: vectors -- list of vectors in an ambient space ambient_space -- VectorSpace_ambient; an optional ambient space; is specified the constructor will work even if the list of vectors is ambient.
ambient_space,
basis,
change_ring,
dimension,
echelonized_basis,
generators,
is_ambient,
linear_combination_of_basis
Further documentation:
R) |
Change this vector space to be a vector space over R by coercing the basis vectors into R. The echelonized basis vectors must coerce into R or this command will fail.
sage: V = VectorSpace(QQ,3) sage: W = V.subspace([V.gen(0) + QQ('1/2')*V.gen(1)]) sage: W.change_ring(GF(7)) Vector space of degree 3, dimension 1 over Finite field of size 7 Basis matrix: [1 4 0]
) |
Return whether this space is ambient, i.e., has dimension the same as its degree.
v) |
Return the linear combination of the basis for self obtained from the coordinates of v.
Instances of class VectorSpace_subspace also have the following special functions:
__contains__
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