33.6 Homspaces between free modules

Module: sage.modules.free_module_homspace

Homspaces between free modules

We create $ \End (\mathbf{Z}^2)$ and compute a basis.

sage: M = FreeModule(IntegerRing(),2)
sage: E = End(M)
sage: B = E.basis()
sage: len(B)
4
sage: B[0]
Free module morphism defined by the matrix
[1 0]
[0 0]
Domain: Ambient free module of rank 2 over the principal ideal domain ...
Codomain: Ambient free module of rank 2 over the principal ideal domain ...

We create $ \Hom (\mathbf{Q}^3, \mathbf{Q}^2)$ and compute a basis.

sage: V3 = VectorSpace(RationalField(),3)
sage: V2 = VectorSpace(RationalField(),2)
sage: H = Hom(V3,V2)
sage: H
Set of Morphisms from Vector space of dimension 3 over Rational Field
to Vector space of dimension 2 over Rational Field in Category of
vector spaces over Rational Field
sage: B = H.basis()
sage: len(B)
6
sage: B[0]
Free module morphism defined by the matrix
[1 0]
[0 0]
[0 0]
Domain: Vector space of dimension 3 over Rational Field
Codomain: Vector space of dimension 2 over Rational Field

Module-level Functions

is_FreeModuleHomspace( x)

Class: FreeModuleHomspace

class FreeModuleHomspace

Functions: basis,$ \,$ identity

basis( self)

Return a basis for this space of free module homomorphisms.

identity( self)

Return identity morphism in an endomorphism ring.

sage: V=VectorSpace(QQ,5)
sage: H=V.Hom(V)
sage: H.identity()
Free module morphism defined by the matrix
[1 0 0 0 0]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
Domain: Vector space of dimension 5 over Rational Field
Codomain: Vector space of dimension 5 over Rational Field

Special Functions: __call__,$ \,$ _coerce_impl,$ \,$ _matrix_space

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