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arXiv · 1907.05024

Improving the Cauchy-Schwarz inequality

Kamal Bhattacharyya
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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.

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Kamal Bhattacharyya. 2019-07-11. Improving the Cauchy-Schwarz inequality. https://doi.org/10.12743/quanta.v8i1.90

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