Variance bounds, with an application to norm bounds for commutators

  title={Variance bounds, with an application to norm bounds for commutators},
  author={Koenraad M. R. Audenaert},
  journal={Linear Algebra and its Applications},
  • K. Audenaert
  • Published 22 July 2009
  • Mathematics
  • Linear Algebra and its Applications
Abstract Murthy and Sethi [M.N. Murthy, V.K. Sethi, Sankhya Ser. B 27 (1965) 201–210] gave a sharp upper bound on the variance of a real random variable in terms of the range of values of that variable. We generalise this bound to the complex case and, more importantly, to the matrix case. In doing so, we make contact with several geometrical and matrix analytical concepts, such as the numerical range, and introduce the new concept of radius of a matrix. We also give a new and simplified proof… Expand

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