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Volume 17, Issue 1 (Jan 2009)

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The Real Vector Spaces of Finite Sequences are Finite Dimensional

Yatsuka Nakamura
  • Shinshu University Nagano, Japan
/ Artur Korniłowicz
  • Institute of Computer Science, University of Białystok, Sosnowa 64, 15-887 Białystok, Poland
/ Nagato Oya
  • Shinshu University Nagano, Japan
/ Yasunari Shidama
  • Shinshu University Nagano, Japan
Published Online: 2009-03-20 | DOI: https://doi.org/10.2478/v10037-009-0001-2

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 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

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About the article


Published Online: 2009-03-20

Published in Print: 2009-01-01



Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-009-0001-2. Export Citation

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