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...