The Real Vector Spaces of Finite Sequences are Finite Dimensional

Yatsuka Nakamura; Artur Korniłowicz; Nagato Oya; Yasunari Shidama

doi:10.2478/v10037-009-0001-2

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The Real Vector Spaces of Finite Sequences are Finite Dimensional

Formalized Mathematics

Volume 17 (2009): Issue 1 (March 2009)

By: Yatsuka Nakamura, Artur Korniłowicz, Nagato Oya and Yasunari Shidama

Open Access

|Mar 2009

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

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Articles in this issue

DOI: https://doi.org/10.2478/v10037-009-0001-2 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 1 - 9

Published on: Mar 20, 2009

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2009 Yatsuka Nakamura, Artur Korniłowicz, Nagato Oya, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 17 (2009): Issue 1 (March 2009)