Jurnal SINTA 3
SISTEM ORTONORMAL DALAM RUANG HILBERT
BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 8 No. 2 (2014) · pp. 19–26
- ISSN
- 2615-3017, 1978-7227
- Published
- 2014-12-01
- Publisher
- PATTIMURA UNIVERSITY
- Language
- eng
Abstract
Hilbert space is one of the important inventions in mathematics. Historically, the theory of Hilbert space originated from David Hilbert’s work on quadratic form in infinitely many variables with their applications to integral equations. This paper contains some definitions such as vector space, normed space and inner product space (also called pre-Hilbert space), and which is important to construct the Hilbert space. The fundamental ideas and results are discussed with special attention given to finite dimensional pre-Hilbert space and some basic propositions of orthonormal systems in Hilbert space. This research found that each finite dimensional pre- Hilbert space is a Hilbert space. We have provided that a finite orthonormal systems in a Hilbert space X is complete if and only if this orthonormal systems is a basis of X.
Collaboration network of the authors
14 authors · 27 co-authorship links
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| Co-author | Organisation | Joint articles |
|---|---|---|
| Elvinus R. Persulessy | Affiliation unknown | 1 |
| Ade M. Telussa | Affiliation unknown | 1 |
| Antonia E. Wokanubun | Affiliation unknown | 1 |
| Berny P. Tomasouw | Affiliation unknown | 1 |
| Salmon N. Aulele | Affiliation unknown | 1 |
| Safriyani Tomia | Affiliation unknown | 1 |
| Mozart W. Talakua | Affiliation unknown | 1 |
| A. W. Taluta | Affiliation unknown | 1 |
| Venn Y. I. Ilwaru | Affiliation unknown | 1 |
| Tesa Sumah | Affiliation unknown | 1 |
| Yopi Andry Lesnussa | Affiliation unknown | 1 |
| Ferry Kondo Lembang | Affiliation unknown | 1 |
| L. Tehuayo | Affiliation unknown | 1 |
Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.