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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| Date: | 2004 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2004
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/156422 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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