# 09covar - EECS 501 COVARIANCE MATRICES Fall 2001 DEF A...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EECS 501 COVARIANCE MATRICES Fall 2001 DEF: A random vector is a vector of random variables ~x = [ x 1 . . . x N ] . Note: Unless otherwise stated, a random vector is a column vector. DEF: The mean vector of random vector ~x is ~ = E [ ~x ] = [ E [ x 1 ] . . . E [ x N ]] . DEF: The covariance matrix K x = x of ~x is the N N matrix whose ( i, j ) th element ( K x ) ij = x i x j = E [ x i x j ]- E [ x i ] E [ x j ]. Note: K x = E [( ~x- E [ ~x ])( ~x- E [ ~x ]) ] = E [ ~x~x ]- E [ ~x ] E [ ~x ] (outer products). Also Outer product ~x~ y = [ x i y j ] = N N matrix having rank 1. Note: Inner product ~x ~ y = x i y i =scalar=Trace of outer product. 1. K x is a symmetric matrix: ( K x ) ij = x i x j = x j x i = ( K x ) ji . 2. K x is a positive semidefinite matrix: For any vector ~a , the scalar ~a K x ~a = N i =1 N j =1 a i ( K x ) ij a j 0. 3. In particular, the diagonal elements of K x have ( K x ) ii = 2 x i 0....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

09covar - EECS 501 COVARIANCE MATRICES Fall 2001 DEF A...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online