Sums of skew-Hamiltonian or Hamiltonian dilatations.
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| Title: | Sums of skew-Hamiltonian or Hamiltonian dilatations. |
|---|---|
| Authors: | de la Cruz, Ralph John L.1 (AUTHOR) rjdelacruz@math.upd.edu.ph, Salinasan, Jenny R.1 (AUTHOR) jsalinasan@math.upd.edu.ph, Tabigue, Mary Anne L.1,2 (AUTHOR) mltabigue@up.edu.ph |
| Source: | Linear Algebra & its Applications. May2026, Vol. 737, p213-226. 14p. |
| Subjects: | Complex matrices, Matrix decomposition, Linear algebra, Matrices (Mathematics), Symplectic geometry |
| Abstract: | A 2 n × 2 n complex matrix A is Hamiltonian (respectively, skew-Hamiltonian) if J − 1 A T J = − A (respectively, J − 1 A T J = A) where J = [ 0 n I n − I n 0 n ]. We say that A is a Hamiltonian dilatation (respectively, skew-Hamiltonian dilatation) if A is Hamiltonian (respectively, skew-Hamiltonian) and is similar to [ a ] ⊕ [ − a ] ⊕ 0 2 n − 2 (respectively, [ a ] ⊕ [ a ] ⊕ 0 2 n − 2) for some 0 ≠ a ∈ C. We show that every 2 n × 2 n nonzero Hamiltonian not similar to J 2 (0) is a sum of n or fewer Hamiltonian dilatations and that for some Hamiltonian, n is sharp. We also show that every 2 n × 2 n nonzero skew-Hamiltonian is a sum of n or fewer skew-Hamiltonian dilatations, and for some skew-Hamiltonian, n is also sharp. Finally, we show that a Hamiltonian similar to J 2 (0) is a sum of two Hamiltonian dilatations and no fewer. [ABSTRACT FROM AUTHOR] |
| Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192196635 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Sums of skew-Hamiltonian or Hamiltonian dilatations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22de+la+Cruz%2C+Ralph+John+L%2E%22">de la Cruz, Ralph John L.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rjdelacruz@math.upd.edu.ph</i><br /><searchLink fieldCode="AR" term="%22Salinasan%2C+Jenny+R%2E%22">Salinasan, Jenny R.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jsalinasan@math.upd.edu.ph</i><br /><searchLink fieldCode="AR" term="%22Tabigue%2C+Mary+Anne+L%2E%22">Tabigue, Mary Anne L.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> mltabigue@up.edu.ph</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. May2026, Vol. 737, p213-226. 14p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Complex+matrices%22">Complex matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+decomposition%22">Matrix decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+algebra%22">Linear algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Symplectic+geometry%22">Symplectic geometry</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A 2 n × 2 n complex matrix A is Hamiltonian (respectively, skew-Hamiltonian) if J − 1 A T J = − A (respectively, J − 1 A T J = A) where J = [ 0 n I n − I n 0 n ]. We say that A is a Hamiltonian dilatation (respectively, skew-Hamiltonian dilatation) if A is Hamiltonian (respectively, skew-Hamiltonian) and is similar to [ a ] ⊕ [ − a ] ⊕ 0 2 n − 2 (respectively, [ a ] ⊕ [ a ] ⊕ 0 2 n − 2) for some 0 ≠ a ∈ C. We show that every 2 n × 2 n nonzero Hamiltonian not similar to J 2 (0) is a sum of n or fewer Hamiltonian dilatations and that for some Hamiltonian, n is sharp. We also show that every 2 n × 2 n nonzero skew-Hamiltonian is a sum of n or fewer skew-Hamiltonian dilatations, and for some skew-Hamiltonian, n is also sharp. Finally, we show that a Hamiltonian similar to J 2 (0) is a sum of two Hamiltonian dilatations and no fewer. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.laa.2026.02.018 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 14 StartPage: 213 Subjects: – SubjectFull: Complex matrices Type: general – SubjectFull: Matrix decomposition Type: general – SubjectFull: Linear algebra Type: general – SubjectFull: Matrices (Mathematics) Type: general – SubjectFull: Symplectic geometry Type: general Titles: – TitleFull: Sums of skew-Hamiltonian or Hamiltonian dilatations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: de la Cruz, Ralph John L. – PersonEntity: Name: NameFull: Salinasan, Jenny R. – PersonEntity: Name: NameFull: Tabigue, Mary Anne L. IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00243795 Numbering: – Type: volume Value: 737 Titles: – TitleFull: Linear Algebra & its Applications Type: main |
| ResultId | 1 |
