Improving the Cauchy–Schwarz Inequality

Kamal Bhattacharyya

Abstract


We highlight overlap as one of the simplest inequalities in linear space that yields a number of useful results. One obtains the Cauchy–Schwarz inequality as a special case. More importantly, a variant of it is seen to work desirably in certain singular situations where the celebrated inequality appears to be useless. The basic tenet generates a few other interesting relations, including the improvements over certain common uncertainty bounds. Role of projection operators in modifying the Cauchy–Schwarz relation is noted. Selected applications reveal the efficacy.

Quanta 2019; 8: 36-43.


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DOI: https://doi.org/10.12743/quanta.v8i1.90

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