On the spectrum and spectrum multiplicities of a sum of orthogonal projections
Let H be a unitary (finite dimensional Hilbert) space. It is known [1] that a self-adjoint operator on H, A = A* ≥ 0, is a sum of n orthogonal projections for some n ∈ N if and only if 1) tr A ∈ N∪{0}, 2) tr A ≥ dim Im A (Im A = AH)
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2004 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2004
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/156422 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the spectrum and spectrum multiplicities of a sum of orthogonal projections / A.A. Kyrychenko, Yu.S. Samoılenko // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 3. — С. 71–76. — Бібліогр.: 9 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862657277312368640 |
|---|---|
| author | Kyrychenko, A.A. Samoılenko, Yu.S. |
| author_facet | Kyrychenko, A.A. Samoılenko, Yu.S. |
| citation_txt | On the spectrum and spectrum multiplicities of a sum of orthogonal projections / A.A. Kyrychenko, Yu.S. Samoılenko // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 3. — С. 71–76. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let H be a unitary (finite dimensional Hilbert) space. It is known [1] that a self-adjoint operator on H, A = A* ≥ 0, is a sum of n orthogonal projections for some n ∈ N if and only if 1) tr A ∈ N∪{0}, 2) tr A ≥ dim Im A (Im A = AH)
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| first_indexed | 2025-12-02T05:42:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156422 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-02T05:42:46Z |
| publishDate | 2004 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Kyrychenko, A.A. Samoılenko, Yu.S. 2019-06-18T13:32:11Z 2019-06-18T13:32:11Z 2004 On the spectrum and spectrum multiplicities of a sum of orthogonal projections / A.A. Kyrychenko, Yu.S. Samoılenko // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 3. — С. 71–76. — Бібліогр.: 9 назв. — англ. 1726-3255 https://nasplib.isofts.kiev.ua/handle/123456789/156422 Let H be a unitary (finite dimensional Hilbert) space. It is known [1] that a self-adjoint operator on H, A = A* ≥ 0, is a sum of n orthogonal projections for some n ∈ N if and only if 1) tr A ∈ N∪{0}, 2) tr A ≥ dim Im A (Im A = AH) en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the spectrum and spectrum multiplicities of a sum of orthogonal projections Article published earlier |
| spellingShingle | On the spectrum and spectrum multiplicities of a sum of orthogonal projections Kyrychenko, A.A. Samoılenko, Yu.S. |
| title | On the spectrum and spectrum multiplicities of a sum of orthogonal projections |
| title_full | On the spectrum and spectrum multiplicities of a sum of orthogonal projections |
| title_fullStr | On the spectrum and spectrum multiplicities of a sum of orthogonal projections |
| title_full_unstemmed | On the spectrum and spectrum multiplicities of a sum of orthogonal projections |
| title_short | On the spectrum and spectrum multiplicities of a sum of orthogonal projections |
| title_sort | on the spectrum and spectrum multiplicities of a sum of orthogonal projections |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156422 |
| work_keys_str_mv | AT kyrychenkoaa onthespectrumandspectrummultiplicitiesofasumoforthogonalprojections AT samoılenkoyus onthespectrumandspectrummultiplicitiesofasumoforthogonalprojections |