The Real Vector Spaces of Finite Sequences are Finite Dimensional
Yatsuka Nakamura ; Artur Korniłowicz ; Nagato Oya ; Yasunari Shidama
Formalized Mathematics, Tome 17 (2009), p. 1-9 / Harvested from The Polish Digital Mathematics Library
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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

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:267003 
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     author = {Yatsuka Nakamura and Artur Korni\l owicz and Nagato Oya and Yasunari Shidama},
     title = {The Real Vector Spaces of Finite Sequences are Finite Dimensional},
     journal = {Formalized Mathematics},
     volume = {17},
     year = {2009},
     pages = {1-9},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0001-2}
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Yatsuka Nakamura; Artur Korniłowicz; Nagato Oya; Yasunari Shidama. The Real Vector Spaces of Finite Sequences are Finite Dimensional. Formalized Mathematics, Tome 17 (2009) pp. 1-9. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0001-2/

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