A new proof of the Benedetti's inequality and some applications to perturbation to real eigenvalues and singular values

Humberto Sarria ^[1] ; Juan Carlos Martínez ^[2]
1. [1] Universidad Nacional de Colombia
  
  Universidad Nacional de Colombia
  
  Colombia
2. [2] Universidad del Rosario
  
  Universidad del Rosario
  
  Colombia
Localización: Boletín de matemáticas, ISSN 0120-0380, ISSN-e 2357-6529, Vol. 23, Nº. 2, 2016, págs. 105-114
Idioma: inglés
Títulos paralelos:
- Una nueva prueba de desigualdad de Benedetti y algunas aplicaciones a la perturbación de valores propios reales y valores singulares
Enlaces
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Resumen
- 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.