Subspaces and Cosets of Subspace of Real Unitary Space

Noboru Endou

Gifu National College of Technology

Takashi Mitsuishi

Miyagi University

Yasunari Shidama

Shinshu University, Nagano

Summary.

In this article, subspace and the coset of subspace of real unitary space are defined. And we discuss some of their fundamental properties.

MML Identifier: RUSUB_1

Contents (PDF format)

1. Definition and Axioms of the Subspace of Real Unitary Space
2. Definition of Zero Subspace and Improper Subspace of Real Unitary Space
3. Theorems of Zero Subspace and Improper Subspace
4. The Cosets of Subspace of Real Unitary Space
5. Theorems of the Cosets

Bibliography

[1] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[2] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[4] Jan Popiolek. Introduction to Banach and Hilbert spaces --- part I. Journal of Formalized Mathematics, 3, 1991.

[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] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.

[8] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

[9] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Journal of Formalized Mathematics, 1, 1989.

[10] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.

[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[12] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.