We shall give a proof of the following result of Oseledec, in which
G
L
(
d
)
GL(d)
denotes the space of invertible
d
×
d
d \times d
real matrices,
|
|
∙
|
|
|| \bullet ||
denotes any norm on the space of
d
×
d
d \times d
matrices, and
log
+
(
t
)
=
max
(
0
,
log
(
t
)
)
{\log ^+ }(t) = \max (0,\log (t))
for
t
∈
[
0
,
∞
)
t \in [0,\infty )
.