33.28 Row Space Basis Records

A vector space basis is a record with at least the following components.

isBasis :

always true,

vectors :

the list of basis vectors,

structure :

the underlying vector space,

operations :

a record that contains the functions for the basis, at least Coefficients, Print, and SiftedVector. Of course these functions depend on the special properties of the basis, so different basis types have different operations record.

Depending on the type of the basis, the basis record additionally contains some components that are assumed and used by the functions in the operations record.

For arbitrary bases these are semiEchelonBasis and basechange, for semi-echelonized bases these are the lists heads and ishead. Furthermore, the booleans isSemiEchelonBasis and isCanonicalBasis may be present.

The operations records for the supported bases are

BasisRowSpaceOps :

for arbitrary bases,

CanonicalBasisRowSpaceOps :

for the canonical basis of a space,

SemiEchelonBasisRowSpaceOps :

for semi-echelonized bases.

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