---
_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: <i>SOFSEM
    2000: Theory and Practice of Informatics</i>. Vol 1963. Berlin, Heidelberg: Springer;
    2000:450-458. doi:<a href="https://doi.org/10.1007/3-540-44411-4_34">10.1007/3-540-44411-4_34</a>'
  apa: 'Ziegler, M., &#38; Brattka, V. (2000). Computing the Dimension of Linear Subspaces.
    In <i>SOFSEM 2000: Theory and Practice of Informatics</i> (Vol. 1963, pp. 450–458).
    Berlin, Heidelberg: Springer. <a href="https://doi.org/10.1007/3-540-44411-4_34">https://doi.org/10.1007/3-540-44411-4_34</a>'
  bibtex: '@inproceedings{Ziegler_Brattka_2000, place={Berlin, Heidelberg}, title={Computing
    the Dimension of Linear Subspaces}, volume={1963}, DOI={<a href="https://doi.org/10.1007/3-540-44411-4_34">10.1007/3-540-44411-4_34</a>},
    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 <i>SOFSEM 2000: Theory and Practice of Informatics</i>, 1963:450–58.
    Berlin, Heidelberg: Springer, 2000. <a href="https://doi.org/10.1007/3-540-44411-4_34">https://doi.org/10.1007/3-540-44411-4_34</a>.'
  ieee: 'M. Ziegler and V. Brattka, “Computing the Dimension of Linear Subspaces,”
    in <i>SOFSEM 2000: Theory and Practice of Informatics</i>, 2000, vol. 1963, pp.
    450–458.'
  mla: 'Ziegler, Martin, and Vasco Brattka. “Computing the Dimension of Linear Subspaces.”
    <i>SOFSEM 2000: Theory and Practice of Informatics</i>, vol. 1963, Springer, 2000,
    pp. 450–58, doi:<a href="https://doi.org/10.1007/3-540-44411-4_34">10.1007/3-540-44411-4_34</a>.'
  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'
...