Computing the Dimension of Linear Subspaces

Authors:
Martin Ziegler;Vasco Brattka
Affiliations:
-;-
Venue:
SOFSEM '00 Proceedings of the 27th Conference on Current Trends in Theory and Practice of Informatics
Year:
2000

Citing 5
Cited 1

Complexity theory of real functions

Complexity theory of real functions
Recursively enumerable subsets of Rq in two computing models: Blum-Shub-Smale machine and Turing machine

Theoretical Computer Science
Computability on subsets of Euclidean space I: closed and compact subsets

Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction

Computable analysis: an introduction
On Extreme Points of Convex Compact Turing Located Set

LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science

A Computable Spectral Theorem

CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis

Quantified Score

Hi-index	0.00

Visualization

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.