A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values
Using the standard deviation of the real samples μn ≥ … ≥ μ1 and λn ≥ … ≥ λ1, we refine the Chebyshev's inequality (refer to [5]),As a consequence, we obtain a new proof of the Benedetti's inequality (refer to [1], [2] and [4])where Cov[μ, λ], s(μ) and s(λ) denote the covariance, and the s...
- Autores:
-
Sarria, Humberto
Martínez, Juan Carlos
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2016
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/61874
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/61874
http://bdigital.unal.edu.co/60686/
- Palabra clave:
- 51 Matemáticas / Mathematics
Chebyshev's inequality
Homand-Weiland's inequality
eigenvalues perturbation
singular value perturbation.
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Sarria, Humberto9db56867-efa9-4cec-a00c-449a13c9ea96300Martínez, Juan Carlosd9304f48-7c15-4818-b6a5-0fb690c10d3b3002019-07-02T20:46:46Z2019-07-02T20:46:46Z2016-07-01ISSN: 2357-6529https://repositorio.unal.edu.co/handle/unal/61874http://bdigital.unal.edu.co/60686/Using the standard deviation of the real samples μn ≥ … ≥ μ1 and λn ≥ … ≥ λ1, we refine the Chebyshev's inequality (refer to [5]),As a consequence, we obtain a new proof of the Benedetti's inequality (refer to [1], [2] and [4])where Cov[μ, λ], s(μ) and s(λ) denote the covariance, and the standard deviations (≠ 0) of the sample vectors μ = (μ1, …, μn) and λ = (λ1, …, λn), respectively.We can also get very interesting applications to eigenvalues and singular values perturbation theory. For some kinds of matrices, the result that we present improves the well known Homand-Weiland's inequality.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticashttps://revistas.unal.edu.co/index.php/bolma/article/view/62218Universidad Nacional de Colombia Revistas electrónicas UN Boletín de MatemáticasBoletín de MatemáticasSarria, Humberto and Martínez, Juan Carlos (2016) A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values. Boletín de Matemáticas, 23 (2). pp. 105-114. ISSN 2357-652951 Matemáticas / MathematicsChebyshev's inequalityHomand-Weiland's inequalityeigenvalues perturbationsingular value perturbation.A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular valuesArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL62218-316296-1-SM.pdfapplication/pdf289895https://repositorio.unal.edu.co/bitstream/unal/61874/1/62218-316296-1-SM.pdf21bb2e643a3cebd87167eedaeccff084MD51THUMBNAIL62218-316296-1-SM.pdf.jpg62218-316296-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg5607https://repositorio.unal.edu.co/bitstream/unal/61874/2/62218-316296-1-SM.pdf.jpga275eed6c3fdc9a3075ffee5a7dd1723MD52unal/61874oai:repositorio.unal.edu.co:unal/618742024-04-20 23:26:14.367Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values |
| title |
A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values |
| spellingShingle |
A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values 51 Matemáticas / Mathematics Chebyshev's inequality Homand-Weiland's inequality eigenvalues perturbation singular value perturbation. |
| title_short |
A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values |
| title_full |
A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values |
| title_fullStr |
A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values |
| title_full_unstemmed |
A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values |
| title_sort |
A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values |
| dc.creator.fl_str_mv |
Sarria, Humberto Martínez, Juan Carlos |
| dc.contributor.author.spa.fl_str_mv |
Sarria, Humberto Martínez, Juan Carlos |
| dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics |
| topic |
51 Matemáticas / Mathematics Chebyshev's inequality Homand-Weiland's inequality eigenvalues perturbation singular value perturbation. |
| dc.subject.proposal.spa.fl_str_mv |
Chebyshev's inequality Homand-Weiland's inequality eigenvalues perturbation singular value perturbation. |
| description |
Using the standard deviation of the real samples μn ≥ … ≥ μ1 and λn ≥ … ≥ λ1, we refine the Chebyshev's inequality (refer to [5]),As a consequence, we obtain a new proof of the Benedetti's inequality (refer to [1], [2] and [4])where Cov[μ, λ], s(μ) and s(λ) denote the covariance, and the standard deviations (≠ 0) of the sample vectors μ = (μ1, …, μn) and λ = (λ1, …, λn), respectively.We can also get very interesting applications to eigenvalues and singular values perturbation theory. For some kinds of matrices, the result that we present improves the well known Homand-Weiland's inequality. |
| publishDate |
2016 |
| dc.date.issued.spa.fl_str_mv |
2016-07-01 |
| dc.date.accessioned.spa.fl_str_mv |
2019-07-02T20:46:46Z |
| dc.date.available.spa.fl_str_mv |
2019-07-02T20:46:46Z |
| dc.type.spa.fl_str_mv |
Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/resource_type/c_6501 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Text |
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http://purl.org/redcol/resource_type/ART |
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http://purl.org/coar/resource_type/c_6501 |
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publishedVersion |
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ISSN: 2357-6529 |
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https://repositorio.unal.edu.co/handle/unal/61874 |
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http://bdigital.unal.edu.co/60686/ |
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ISSN: 2357-6529 |
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https://repositorio.unal.edu.co/handle/unal/61874 http://bdigital.unal.edu.co/60686/ |
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spa |
| language |
spa |
| dc.relation.spa.fl_str_mv |
https://revistas.unal.edu.co/index.php/bolma/article/view/62218 |
| dc.relation.ispartof.spa.fl_str_mv |
Universidad Nacional de Colombia Revistas electrónicas UN Boletín de Matemáticas Boletín de Matemáticas |
| dc.relation.references.spa.fl_str_mv |
Sarria, Humberto and Martínez, Juan Carlos (2016) A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values. Boletín de Matemáticas, 23 (2). pp. 105-114. ISSN 2357-6529 |
| dc.rights.spa.fl_str_mv |
Derechos reservados - Universidad Nacional de Colombia |
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http://purl.org/coar/access_right/c_abf2 |
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Atribución-NoComercial 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc/4.0/ |
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info:eu-repo/semantics/openAccess |
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