To understand the linearity in the covariance definition, we can consider that features c
X2
are a linear function of c
X1
. That is, c
X2
= Ac
X1
+B for A, an arbitrary constant, and B,an
arbitrary column vector. Thus, according to Equation 12.11,
E
c
X1
c
X2
=E
Ac
T
X1
c
X1
+c
T
X1
B
(12.13)
We also have that
E
c
X1
E
c
X2
=AE
c
X1
2
+E
B
E
c
X1