Triangle Inequality

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Triangle Inequality

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Triangle Inequality

The triangle inequality states that the length of any side of a triangle is less than or equal to the sum of the lengths of the other two sides, with equality occurring only when the triangle degenerates to a line. In ${\, this becomes

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We can show this quickly using the Schwarz Inequality.
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