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# Random Vectors

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Vectors  ::  Covariance  ::  Functions  ::  Application  ::  Markov Model

## Covariance

Suppose and (that is, and are random vectors of dimension and , respectively).

Note: is frequently used as a symbol to denote covariance. It should not be confused with a summation sign, and is usually clear from context.

Property:

If is and is and and then

is called the covariance of .'' It is a symmetric matrix, non-negative definite (or positive semidefinite), and thus has all non-negative eigenvalues.

If are mutually uncorrelated then

where

Suppose we partition of dimensions as

of and elements, respectively. let

where and . Similarly,

where

or, in general,

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 31). Random Vectors. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/lec3_2.html. This work is licensed under a Creative Commons License