MATLAB Function Reference Volume 1: A - E - Bad Request

cov
2cov
Purpose Covariance matrix
Syntax C = cov(X)
C = cov(x,y)
Description C = cov(x) where x is a vector returns the variance of the vector elements. For
matrices where each row is an observation and each column a variable, cov(x)
is the covariance matrix. diag(cov(x)) is a vector of variances for each
column, and sqrt(diag(cov(x))) is a vector of standard deviations.
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C = cov(x,y), where x and y are column vectors of equal length, is equivalent
to cov([x y]).
Remarks cov removes the mean from each column before calculating the result.
The covariance function is defined as
where E is the mathematical expectation and µ i =
Exi .
Examples Consider A = [-1 1 2 ; -2 3 1 ; 4 0 3]. To obtain a vector of variances for
each column of A:
See Also corrcoef, mean, std
cov( x1 ,x2 ) = E[ ( x1 – µ 1)
( x2 – µ 2)
]
v = diag(cov(A))'
v =
10.3333 2.3333 1.0000
Compare vector v with covariance matrix C:
C =
10.3333 -4.1667 3.0000
-4.1667 2.3333 -1.5000
3.0000 -1.5000 1.0000
The diagonal elements C(i,i) represent the variances for the columns of A.
The off-diagonal elements C(i,j) represent the covariances of columns i and
j.
xcorr, xcov in the Signal Processing Toolbox