AN ALGEBRAIC APPROACH O HE CONSTRUCTION OF POLYHEDRAL INVARIANT CONES.
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| Title: | AN ALGEBRAIC APPROACH O HE CONSTRUCTION OF POLYHEDRAL INVARIANT CONES. |
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| Authors: | Valcher, Maria Elena1 elena.valcher@unile.it, Farina, Lorenzo2 farina@dis.uniroma1.it |
| Source: | SIAM Journal on Matrix Analysis & Applications. 2000, Vol. 22 Issue 2, p453-471. 19p. |
| Subjects: | Polyhedra models, Radius (Geometry), Eigenvalues, Matrices (Mathematics), Polyhedral functions, Mathematics |
| Abstract: | In this paper, based on algebraic arguments, a new proof of the spectral characterization of those real matrices that leave a proper polyhedral cone invariant [Trans. Amer. Math. Soc., 343 (1994), pp. 479–524] is given. The proof is a constructive one, as it allows us to explicitly obtain for every matrix A, which satisfies the aforementioned spectral requirements, an A-invariant proper polyhedral cone Κ. Some new results are also presented, concerning the way A acts on the cone Κ. In particular, Κ-irreducibility, Κ-primitivity, and Κ-positivity are fully characterized. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Matrix Analysis & Applications is the property of Society for Industrial & Applied Mathematics 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 |
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| Items | – Name: Title Label: Title Group: Ti Data: AN ALGEBRAIC APPROACH O HE CONSTRUCTION OF POLYHEDRAL INVARIANT CONES. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Valcher%2C+Maria+Elena%22">Valcher, Maria Elena</searchLink><relatesTo>1</relatesTo><i> elena.valcher@unile.it</i><br /><searchLink fieldCode="AR" term="%22Farina%2C+Lorenzo%22">Farina, Lorenzo</searchLink><relatesTo>2</relatesTo><i> farina@dis.uniroma1.it</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Matrix+Analysis+%26+Applications%22">SIAM Journal on Matrix Analysis & Applications</searchLink>. 2000, Vol. 22 Issue 2, p453-471. 19p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Polyhedra+models%22">Polyhedra models</searchLink><br /><searchLink fieldCode="DE" term="%22Radius+%28Geometry%29%22">Radius (Geometry)</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Polyhedral+functions%22">Polyhedral functions</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, based on algebraic arguments, a new proof of the spectral characterization of those real matrices that leave a proper polyhedral cone invariant [Trans. Amer. Math. Soc., 343 (1994), pp. 479–524] is given. The proof is a constructive one, as it allows us to explicitly obtain for every matrix A, which satisfies the aforementioned spectral requirements, an A-invariant proper polyhedral cone Κ. Some new results are also presented, concerning the way A acts on the cone Κ. In particular, Κ-irreducibility, Κ-primitivity, and Κ-positivity are fully characterized. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Matrix Analysis & Applications is the property of Society for Industrial & Applied Mathematics 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: 10.1137/S0895479898335465 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 453 Subjects: – SubjectFull: Polyhedra models Type: general – SubjectFull: Radius (Geometry) Type: general – SubjectFull: Eigenvalues Type: general – SubjectFull: Matrices (Mathematics) Type: general – SubjectFull: Polyhedral functions Type: general – SubjectFull: Mathematics Type: general Titles: – TitleFull: AN ALGEBRAIC APPROACH O HE CONSTRUCTION OF POLYHEDRAL INVARIANT CONES. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Valcher, Maria Elena – PersonEntity: Name: NameFull: Farina, Lorenzo IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: 2000 Type: published Y: 2000 Identifiers: – Type: issn-print Value: 08954798 Numbering: – Type: volume Value: 22 – Type: issue Value: 2 Titles: – TitleFull: SIAM Journal on Matrix Analysis & Applications Type: main |
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