Volume 14, 2002

University of Bialystok

Copyright (c) 2002 Association of Mizar Users

**Noboru Endou**- Gifu National College of Technology
**Takashi Mitsuishi**- Miyagi University
**Yasunari Shidama**- Shinshu University, Nagano

- In this article, we mainly discuss linear combination of vectors in Real Unitary Space and dimension of the space. As the result, we obtain some theorems that are similar to those in Real Linear Space.

- Definition and Fundamental Properties of Linear Combination
- Definition of the Basis of Real Unitary Space
- Some Theorems of Lin, Sum, Carrier
- Subspaces of Real Unitary Space Generated by One, Two, or Three Vectors
- Auxiliary Theorems

- [1]
Grzegorz Bancerek.
The ordinal 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]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama.
Operations on subspaces in real unitary space.
*Journal of Formalized Mathematics*, 14, 2002. - [8]
Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama.
Subspaces and cosets of subspace of real unitary space.
*Journal of Formalized Mathematics*, 14, 2002. - [9]
Jan Popiolek.
Introduction to Banach and Hilbert spaces --- part I.
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Andrzej Trybulec.
Tarski Grothendieck set theory.
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Andrzej Trybulec.
Function domains and Fr\aenkel operator.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [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.
Basis of real linear space.
*Journal of Formalized Mathematics*, 2, 1990. - [16]
Wojciech A. Trybulec.
Linear combinations in real linear space.
*Journal of Formalized Mathematics*, 2, 1990. - [17]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [18]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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