Complex Analysis: Theory and Applications · Problem 1.3.18

Complex Numbers — Howell & Matthews

Mathematics — Complex Analysis · cauchy-schwarz-inequality

Problem

Prove the Cauchy-Schwarz inequality: ∣∑k=1nzkwk∣≤∑k=1n∣zk∣2 ∑k=1n∣wk∣2.\left|\sum_{k=1}^n z_k w_k\right| \leq \sqrt{\sum_{k=1}^n |z_k|^2}\, \sqrt{\sum_{k=1}^n |w_k|^2}.

Related theory

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