---
_id: '18146'
abstract:
- lang: eng
text: '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.'
author:
- first_name: Martin
full_name: Ziegler, Martin
last_name: Ziegler
- first_name: Vasco
full_name: Brattka, Vasco
last_name: Brattka
citation:
ama: 'Ziegler M, Brattka V. Computing the Dimension of Linear Subspaces. In: *SOFSEM
2000: Theory and Practice of Informatics*. Vol 1963. Berlin, Heidelberg: Springer;
2000:450-458. doi:10.1007/3-540-44411-4_34'
apa: 'Ziegler, M., & Brattka, V. (2000). Computing the Dimension of Linear Subspaces.
In *SOFSEM 2000: Theory and Practice of Informatics* (Vol. 1963, pp. 450–458).
Berlin, Heidelberg: Springer. https://doi.org/10.1007/3-540-44411-4_34'
bibtex: '@inproceedings{Ziegler_Brattka_2000, place={Berlin, Heidelberg}, title={Computing
the Dimension of Linear Subspaces}, volume={1963}, DOI={10.1007/3-540-44411-4_34},
booktitle={SOFSEM 2000: Theory and Practice of Informatics}, publisher={Springer},
author={Ziegler, Martin and Brattka, Vasco}, year={2000}, pages={450–458} }'
chicago: 'Ziegler, Martin, and Vasco Brattka. “Computing the Dimension of Linear
Subspaces.” In *SOFSEM 2000: Theory and Practice of Informatics*, 1963:450–58.
Berlin, Heidelberg: Springer, 2000. https://doi.org/10.1007/3-540-44411-4_34.'
ieee: 'M. Ziegler and V. Brattka, “Computing the Dimension of Linear Subspaces,”
in *SOFSEM 2000: Theory and Practice of Informatics*, 2000, vol. 1963, pp.
450–458.'
mla: 'Ziegler, Martin, and Vasco Brattka. “Computing the Dimension of Linear Subspaces.”
*SOFSEM 2000: Theory and Practice of Informatics*, vol. 1963, Springer, 2000,
pp. 450–58, doi:10.1007/3-540-44411-4_34.'
short: 'M. Ziegler, V. Brattka, in: SOFSEM 2000: Theory and Practice of Informatics,
Springer, Berlin, Heidelberg, 2000, pp. 450–458.'
date_created: 2020-08-24T09:58:56Z
date_updated: 2022-01-06T06:53:26Z
department:
- _id: '63'
doi: 10.1007/3-540-44411-4_34
intvolume: ' 1963'
language:
- iso: eng
page: 450-458
place: Berlin, Heidelberg
publication: 'SOFSEM 2000: Theory and Practice of Informatics'
publication_identifier:
isbn:
- '9783540413486'
- '9783540444114'
issn:
- 0302-9743
publication_status: published
publisher: Springer
status: public
title: Computing the Dimension of Linear Subspaces
type: conference
user_id: '15415'
volume: 1963
year: '2000'
...