The Real Vector Spaces of Finite Sequences are Finite Dimensional

Yatsuka Nakamura; Artur Korniłowicz; Nagato Oya; Yasunari Shidama

Formalized Mathematics (2009)

  • Volume: 17, Issue: 1, page 1-9
  • ISSN: 1426-2630

Abstract

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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

How to cite

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Yatsuka Nakamura, et al. "The Real Vector Spaces of Finite Sequences are Finite Dimensional." Formalized Mathematics 17.1 (2009): 1-9. <http://eudml.org/doc/267003>.

@article{YatsukaNakamura2009,
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},
author = {Yatsuka Nakamura, Artur Korniłowicz, Nagato Oya, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {1-9},
title = {The Real Vector Spaces of Finite Sequences are Finite Dimensional},
url = {http://eudml.org/doc/267003},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Yatsuka Nakamura
AU - Artur Korniłowicz
AU - Nagato Oya
AU - Yasunari Shidama
TI - The Real Vector Spaces of Finite Sequences are Finite Dimensional
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 1
SP - 1
EP - 9
AB - 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
LA - eng
UR - http://eudml.org/doc/267003
ER -

References

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