Cauchy - Schwarz inequality

Chinese equivalent: 柯西 - 施瓦茨不等式

Cauchy - Schwarz inequality For real or complex vectors, (∑(i = 1)^n a i b i ight)² ≤ (∑(i = 1)^n a i² ight)(∑(i = 1)^n b i² ight).

Syllabus path: Sets and Inequalities › Basic Properties and Solutions of Inequalities › The AM-GM Inequality

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CSCA Mathematics Exam Glossary

Definition

Cauchy - Schwarz inequality For real or complex vectors, (∑(i = 1)^n a i b i ight)² ≤ (∑(i = 1)^n a i² ight)(∑(i = 1)^n b i² ight).

Related tutorial and examples

The AM-GM Inequality

The AM - GM Inequality In the CSCA exam, the AM - GM Inequality (Arithmetic Mean - Geometric Mean) is the nuclear weapon for solving optimization problems (Max/Min), especially those involving reciprocal relationships (like x and (1)/(x) ). 1. Core Formula For any two positive re…

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