---
res:
bibo_abstract:
- 'Since its very beginning, linear algebra is a highly algorithmic subject. Let
us just mention the famous Gauss Algorithm which was invented before the theory
of algorithms has been developed. The purpose of this paper is to link linear
algebra explicitly to computable analysis, that is the theory of computable real
number functions. Especially, we will investigate in which sense the dimension
of a given linear subspace can be computed. The answer highly depends on how the
linear subspace is given: if it is given by a finite number of vectors whose linear
span represents the space, then the dimension does not depend continuously on
these vectors and consequently it cannot be computed. If the linear subspace is
represented via its distance function, which is a standard way to represent closed
subspaces in computable analysis, then the dimension does computably depend on
the distance function.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Martin
foaf_name: Ziegler, Martin
foaf_surname: Ziegler
- foaf_Person:
foaf_givenName: Vasco
foaf_name: Brattka, Vasco
foaf_surname: Brattka
bibo_doi: 10.1007/3-540-44411-4_34
bibo_volume: 1963
dct_date: 2000^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0302-9743
- http://id.crossref.org/issn/9783540413486
- http://id.crossref.org/issn/9783540444114
dct_language: eng
dct_publisher: Springer@
dct_title: Computing the Dimension of Linear Subspaces@
...