The Cauchy Schwarz inequality is essential for all of real analysis, and it has several important applications, including the Heisenberg Uncertainty Principle and Normalized Cross Correlation. In this video we give two proofs of the Cauchy Schwarz inequality, and examine an exercise and an application.
Thanks to @oʞoʎos and @chaoshengzhe for catching a couple of errors and omissions in the first version of this video.
//Books
Michael Steele - The Cauchy Schwarz Master Class - amzn.to/3jeAny2
Walter Rudin - Principles of Mathematical Analysis 3rd Edition - amzn.to/3MDHUis
Gerald Folland - Real Analysis: Modern Techniques and Their Applications - amzn.to/3JmK6Np
R. Shankar - Principles of Quantum Mechanics - amzn.to/40825xj
Maxwell Rosenlicht - Introduction to Analysis - amzn.to/3NFYiAC
Tom Apostol - Mathematical Analysis 2nd Edition - amzn.to/3mwxFlC
//Exercises
- Can you find another application of Cauchy Schwarz? Scour the internet and share with us in the comments!
//MATLAB Code
bitbucket.org/joelrosenfeld/c...
//Watch Next
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0:00 Introduction
1:21 First Proof
4:32 Use Example
5:51 Second Proof
10:36 Normalized Cross Correlation
12:32 Wrap Up
Негізгі бет Cauchy Schwarz and what to DO with it (corrected) // An Introduction to Real Analysis
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