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

Wojciech A. Trybulec

Warsaw University

Supported by RPBP.III24.C1.
Summary.

Sum, direct sum and intersection of subspaces are introduced. We prove
some theorems concerning those notions and the decomposition of vector
onto two subspaces. Linear complement of a subspace is also defined. We prove
theorems that belong rather to [4].
The terminology and notation used in this paper have been
introduced in the following articles
[6]
[3]
[9]
[1]
[10]
[2]
[12]
[11]
[7]
[4]
[5]
[8]
Contents (PDF format)
Bibliography
 [1]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Andrzej Trybulec.
Domains and their Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [7]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Wojciech A. Trybulec.
Subspaces and cosets of subspaces in vector space.
Journal of Formalized Mathematics,
2, 1990.
 [9]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Stanislaw Zukowski.
Introduction to lattice theory.
Journal of Formalized Mathematics,
1, 1989.
Received July 27, 1990
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