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.III-24.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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