Correlation Angles and Inner Products: Application to a Problem from   Physics
  Covariance is used as an inner product on a formal vector space built on n random variables to define measures of correlation Md 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. 
David H. Douglass, Jonathan Pakianathan, Adam Towsley
stat.AP math.MG