December 2014
Intermediate to advanced
908 pages
37h 38m
English
Content preview from Principles of System Identification
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166 Principles of System Identification: Theory and Practice
Covariance of vector quantities
The measure can be extended to a vector of random variables in a straightforward manner to obtain
a variance-covariance (or simply covariance) matrix.
For a vector of random variables,
X =
f
X
1
X
2
··· X
N
g
T
the covariance matrix is given by
Σ
X
= E ((X − µ
X
)(X − µ
X
)
T
) (7.30)
=
σ
2
X
1
σ
X
1
X
2
··· σ
X
1
X
N
σ
X
2
X
1
σ
2
X
2
··· σ
X
2
X
N
.
.
. ··· ···
.
.
.
σ
X
N
X
1
σ
X
N
X
2
··· σ
2
X
N
(7.31)
The diagonal of Σ
X
contains variance of individual RVs while the off-diagonals contain covariance
between a pair of RVs.
The variance-covariance matrix is one of the most widely encountered quantities