<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">In this paper we show the finite dimensionality of real linear spaces with their carriers equal R<italic>n</italic>. We also give the standard basis of such spaces. For the set R<italic>n</italic> we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed spaces is proved to equal <italic>n</italic>.MML identifier: EUCLID 7, version: 7.11.01 4.117.1046</abstract>

In this paper we show the finite dimensionality of real linear spaces with their carriers equal Rn. We also give the standard basis of such spaces. For the set Rn we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed spaces is proved to equal n.MML identifier: EUCLID 7, version: 7.11.01 4.117.1046

The Real Vector Spaces of Finite Sequences are Finite Dimensional

Institute of Computer Science, University of Białystok, Sosnowa 64, 15-887 Białystok, Poland

Formalized Mathematics

{"article-title":"The Real Vector Spaces of Finite Sequences are Finite Dimensional"}

In this paper we show the finite dimensionality of real linear spaces with their carriers equal Rn. We also give the standard basis of such spaces. For the set...

The Real Vector Spaces of Finite Sequences are Finite Dimensional

Published Online: Mar 20, 2009

Page range: 1 - 9

DOI: https://doi.org/10.2478/v10037-009-0001-2

This content is open access.