施瓦茨不等式的应用

AbstractCauchy-Schwartz Inequality is one of the most important inequalities in mathematicalanalysis,which is widely used in many different fields.In this paper,several commonexpressions of Cauchy -Schwartz Inequality are summarized,and the corresponding proofs aregiven,and the generalization of Cauchy-Schwartz Inequality is systematically discussed.On thisbasis,this paper presents the application of Cauchy -Schwartz Inequality in probability statisticsand machine learning.At the end of the paper,the more general form of Cauchy -SchwartzInequality,namely,Holder Inequality,and its application are given.Keyword Cauchy-Schwarz inequality,probability theory and statistics,machine learning,Holder inequality.第2页