5.1.1.4 VectorSpace_subspace Objects

class VectorSpace_subspace
The VectorSpace_subspace class defines functionality for subspaces of ambient vector spaces over an arbitrary base field. This class derives from VectorSpace_generic.
VectorSpace_subspace( 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.

Instances of class VectorSpace_subspace have the following functions (in addition to inherited functions and special functions):

ambient_space,$  $ basis,$  $ change_ring,$  $ dimension,$  $ echelonized_basis,$  $ generators,$  $ is_ambient,$  $ linear_combination_of_basis

Further documentation:

change_ring( 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]

is_ambient( )

Return whether this space is ambient, i.e., has dimension the same as its degree.

linear_combination_of_basis( 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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