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

Wojciech A. Trybulec

Warsaw University
Summary.

Notions of linear independence and dependence
of set of vectors, the subspace generated by a set of vectors
and basis of real linear space are introduced.
Some theorems concerning those notions are proved.
The terminology and notation used in this paper have been
introduced in the following articles
[8]
[6]
[16]
[10]
[3]
[17]
[2]
[4]
[5]
[14]
[9]
[7]
[13]
[12]
[11]
[15]
[1]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
Cardinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [9]
Andrzej Trybulec.
Function domains and Fr\aenkel operator.
Journal of Formalized Mathematics,
2, 1990.
 [10]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [11]
Wojciech A. Trybulec.
Operations on subspaces in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Wojciech A. Trybulec.
Partially ordered sets.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Wojciech A. Trybulec.
Subspaces and cosets of subspaces in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [15]
Wojciech A. Trybulec.
Linear combinations in real linear space.
Journal of Formalized Mathematics,
2, 1990.
 [16]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [17]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received July 10, 1990
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