base_field, degree, [sparse=False]) |
INPUT:: base_field -- Ring; a field degree -- int >= 0; the degree of the vector space (number of components of vectors). sparse -- bool; whether or not vectors are given a sparse representation (default: False)
ambient_space,
basis,
change_ring,
dimension,
echelonized_basis,
is_ambient,
is_subspace,
linear_combination_of_basis
Further documentation:
) |
sage: V = VectorSpace(RationalField(), 2); V Full Vector space of degree 2 over Rational Field sage: V.basis() [(1, 0), (0, 1)]
R) |
Change this vector space to be a vector space over R by coercing the basis vectors into R.
sage: V = VectorSpace(RationalField(),3) sage: V.change_ring(GF(7)) Full Vector space of degree 3 over Finite field of size 7
) |
sage: V = VectorSpace(RationalField(), 2); V Full Vector space of degree 2 over Rational Field sage: V.basis() [(1, 0), (0, 1)]
other) |
True if this vector space is a subspace of other.
sage: V = VectorSpace(QQ, 3) sage: W = V.subspace([V.gen(0), V.gen(0) + V.gen(1)]) sage: V.is_subspace(W) False sage: W = VectorSpace(QQ, 2) sage: W.is_subspace(V) False
v) |
Return the linear combination of the basis for self obtained from the coordinates of v.
Instances of class VectorSpace_ambient also have the following special functions:
__contains__
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