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

Wojciech A. Trybulec

Warsaw University

Supported by RPBP.III24.C1.
Summary.

The notion of linear combination of vectors is introduced as a function
from the carrier of a vector space to the carrier of the field. Definition
of linear combination of set of vectors is also presented. We define
addition and subtraction of combinations and multiplication of combination
by element of the field. Sum of finite set of vectors and sum of
linear combination is defined. We prove theorems that belong rather
to [6].
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[12]
[5]
[2]
[13]
[3]
[4]
[8]
[1]
[9]
[6]
[10]
[11]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
Cardinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Functions from a set to a set.
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.
Pigeon hole principle.
Journal of Formalized Mathematics,
2, 1990.
 [11]
Wojciech A. Trybulec.
Subspaces and cosets of subspaces in vector space.
Journal of Formalized Mathematics,
2, 1990.
 [12]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received July 27, 1990
[
Download a postscript version,
MML identifier index,
Mizar home page]