Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

Dimension of Real Unitary Space


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

Summary.

In this article we describe the dimension of real unitary space. Most of theorems are restricted from real linear space. In the last section, we introduce affine subset of real unitary space.

MML Identifier: RUSUB_4

The terminology and notation used in this paper have been introduced in the following articles [14] [13] [19] [10] [2] [3] [4] [1] [5] [11] [16] [6] [15] [18] [12] [17] [9] [8] [7]

Contents (PDF format)

  1. Finite-dimensional Real Unitary Space
  2. Dimension of Real Unitary Space
  3. Fixed-dimensional Subspace Family
  4. Affine Set

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The fundamental properties of natural 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] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[7] Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Linear combinations in real unitary space. Journal of Formalized Mathematics, 14, 2002.
[8] Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Operations on subspaces in real unitary space. Journal of Formalized Mathematics, 14, 2002.
[9] Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Subspaces and cosets of subspace of real unitary space. Journal of Formalized Mathematics, 14, 2002.
[10] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[11] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[12] Jan Popiolek. Introduction to Banach and Hilbert spaces --- part I. Journal of Formalized Mathematics, 3, 1991.
[13] Andrzej Trybulec. Enumerated sets. Journal of Formalized Mathematics, 1, 1989.
[14] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[15] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Journal of Formalized Mathematics, 1, 1989.
[16] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[17] Wojciech A. Trybulec. Basis of real linear space. Journal of Formalized Mathematics, 2, 1990.
[18] Wojciech A. Trybulec. Linear combinations in real linear space. Journal of Formalized Mathematics, 2, 1990.
[19] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

Received October 9, 2002

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