Editing Covariance matrix (section)

===Conflicting nomenclatures and notations===
Nomenclatures differ. Some statisticians, following the probabilist [[William Feller]] in his two-volume book ''An Introduction to Probability Theory and Its Applications'',<ref name="Feller1971">{{cite book|author=William Feller|title=An introduction to probability theory and its applications|url=https://books.google.com/books?id=K7kdAQAAMAAJ|access-date=10 August 2012|year=1971|publisher=Wiley|isbn=978-0-471-25709-7}}</ref>  call the matrix <math>\operatorname{K}_{\mathbf{X}\mathbf{X}}</math> the '''variance''' of the random vector <math>\mathbf{X}</math>, because it is the natural generalization to higher dimensions of the 1-dimensional variance. Others call it the '''covariance matrix''', because it is the matrix of covariances between the scalar components of the vector <math>\mathbf{X}</math>.
<math display="block">
\operatorname{var}(\mathbf{X})
=
\operatorname{cov}(\mathbf{X},\mathbf{X})
=
\operatorname{E}
\left[
 (\mathbf{X} - \operatorname{E} [\mathbf{X}])
 (\mathbf{X} - \operatorname{E} [\mathbf{X}])^\mathsf{T}
\right].
</math>

Both forms are quite standard, and there is no ambiguity between them. The matrix <math>\operatorname{K}_{\mathbf{X}\mathbf{X}}</math> is also often called the '''variance-covariance matrix''', since the diagonal terms are in fact variances.

By comparison, the notation for the [[cross-covariance matrix]] ''between'' two vectors is 
<math display="block">
\operatorname{cov}(\mathbf{X},\mathbf{Y})