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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 16, 2015

Antieigenvalue analysis for continuum mechanics, economics, and number theory

Karl Gustafson
From the journal Special Matrices

Abstract

My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly my matrix maximum turning angle of the stress tensor of the material. The important Sharpe ratio of the Capital Asset Pricing Model is now seen in terms of my antieigenvalue theory. Euclid’s Formula for Pythagorean triples becomes a special case of my operator trigonometry.

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Received: 2015-7-26
Accepted: 2015-10-19
Published Online: 2015-12-16
Published in Print: 2016-1-1

© 2016 Karl Gustafson, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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