Let be a
field,
a
-vector space,
and
-
a
linear mapping. Then the mapping
-
has the following properties.
- For a constant polynomial
,
we have
-
In particular, the zero polynomial is sent to the zero mapping and the constant -polynomial is sent to the identity.
- We have
-
for all polynomials
.
- We have
-
for all polynomials
.
- We have
-
for all
.