Computing the Dimension of Linear Subspaces
Ziegler, Martin
Brattka, Vasco
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.
Springer
2000
info:eu-repo/semantics/conferenceObject
doc-type:conferenceObject
text
http://purl.org/coar/resource_type/c_5794
https://ris.uni-paderborn.de/record/18146
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>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1007/3-540-44411-4_34
info:eu-repo/semantics/altIdentifier/issn/0302-9743
info:eu-repo/semantics/altIdentifier/isbn/9783540413486
info:eu-repo/semantics/altIdentifier/isbn/9783540444114
info:eu-repo/semantics/closedAccess