Page 32 - Introduction to Statistical Pattern Recognition
P. 32
14 Introduction to Statistical Pattern Recognition
defined by
X = E ( (X-M)(X-M)T) = E
m,) ...
ml) ...
(2.13)
The components cI, of this matrix are
(2.14)
Thus, the diagonal components of the covariance matrix are the \w.iunces of
individual random variables, and the off-diagonal components are the coi~~ri-
unces of two random variables, xi and x,. Also, it should be noted that all
covariance matrices are symmetric. This property allows us to employ results
from the theory of symmetric matrices as an important analytical tool.
Equation (2.13) is often converted into the following form:
