Cauchy-schwarz functionals
نویسندگان
چکیده
منابع مشابه
A Generalized Cauchy–schwarz Inequality
In the course of realizing certain triangle centers as points that minimize certain quantities, C. Kimberling and P. Moses, in Math. Mag. 85 (2012) 221–227, discovered an inequality in three variables that generalizes the Cauchy-Schwarz inequality, and made a conjecture regarding a generalization of that inequality to an arbitrary number of variables. In this paper, we give a proof of a stronge...
متن کاملGeneralizations of Cauchy-schwarz in Probability Theory
We explore two generalizations of the Cauchy-Schwarz Bessel’s inequality and the Selberg inequality and their application to probability theory. We then give a tautological proof of the De Caen-Selberg Inequality and a proof of the second Borel-Cantelli Lemma with negative dependence. We finish with a suggestion of how linear operator theory can help us understand the tightness of many Selberg-...
متن کاملClassical Coding and the Cauchy-schwarz Inequality
In classical coding, a single quantum state is encoded into classical information. Decoding this classical information in order to regain the original quantum state is known to be impossible. However, one can attempt to construct a state which comes as close as possible. We give bounds on the smallest possible trace distance between the original and the decoded state which can be reached. We gi...
متن کاملInequalities related to the Cauchy-Schwarz inequality
We obtain an inequality complementary to the Cauchy-Schwarz inequality in Hilbert space. The inequalities involving first three powers of a self-adjoint operator are derived. The inequalities include the bounds for the third central moment, as a special case. It is shown that an upper bound for the spectral radius of a matrix is a root of a particular cubic equation, provided all eigenvalues ar...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2000
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700019006