Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 323864, 12 pages
http://dx.doi.org/10.5402/2011/323864
Research Article

Correlation Angles and Inner Products: Application to a Problem from Physics

1Department of Mathematics, University of Rochester, Rochester, NY 14627, USA
2Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA

Received 30 June 2011; Accepted 9 August 2011

Academic Editors: E. Tian, E. Yee, and Y.-G. Zhao

Copyright © 2011 Adam Towsley et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Covariance is used as an inner product on a formal vector space built on 𝑛 random variables to define measures of correlation 𝑀 𝑑 across a set of vectors in a 𝑑 -dimensional space. For 𝑑 = 1 , one has the diameter; for 𝑑 = 2 , one has an area. These concepts are directly applied to correlation studies in climate science.