5.1.1.5 VectorSpace_subspace_with_basis Objects

class VectorSpace_subspace_with_basis
The VectorSpace_subspace_with_basis class derives from VectorSpace_subspace and provides additional functionality for subspaces with a specified basis, which need not be in echelon form.
VectorSpace_subspace_with_basis( basis, [ambient=None])

Instances of class VectorSpace_subspace_with_basis have the following methods (in addition to inherited methods and special methods):

basis,$  $ coordinates,$  $ echelonized_basis,$  $ user_basis

These methods are defined as follows:

basis( )

coordinates( v)

Write v in terms of the user basis for self.

Returns a list c such that if B is the basis for self, then sum c[i] B[i] = v If v is not in self, raises an ArithmeticError exception.

echelonized_basis( )

user_basis( )

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