Improving the Cauchy–Schwarz Inequality
作者: Kamal Bhattacharyya
作者单位: 1Harish-Chandra Research Institute
刊名: Quanta, 2019, Vol.8 (1), pp.36-43
来源数据库: Quanta
DOI: 10.12743/quanta.v8i1.90
原始语种摘要: 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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  • Schwarz 施瓦兹的
  • certain 确实的
  • operators 操作符
  • inequality 不等式
  • relations 性行为
  • uncertainty 不定
  • projection 投射
  • modifying 修改
  • highlight 增强亮度
  • common 普通