Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Basis of Vector Space

Wojciech A. Trybulec

Warsaw University

Supported by RPBP.III24.C1.
Summary.

We prove the existence of a basis of a vector space, i.e., a set of vectors that
generates the vector space and is linearly independent. We
also introduce the notion of a subspace generated by a set of vectors
and linear independence of set of vectors.
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[4]
[14]
[15]
[2]
[3]
[8]
[5]
[1]
[9]
[6]
[10]
[13]
[12]
[11]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [8]
Andrzej Trybulec.
Function domains and Fr\aenkel operator.
Journal of Formalized Mathematics,
2, 1990.
 [9]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Wojciech A. Trybulec.
Linear combinations in real linear space.
Journal of Formalized Mathematics,
2, 1990.
 [11]
Wojciech A. Trybulec.
Linear combinations in vector space.
Journal of Formalized Mathematics,
2, 1990.
 [12]
Wojciech A. Trybulec.
Operations on subspaces in vector space.
Journal of Formalized Mathematics,
2, 1990.
 [13]
Wojciech A. Trybulec.
Subspaces and cosets of subspaces in vector space.
Journal of Formalized Mathematics,
2, 1990.
 [14]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [15]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received July 27, 1990
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