16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 4.2.8

Polynomials

Mathematics — Linear Algebra · composition-map-polynomial

Problem

F

is a field and

h

is a polynomial over

F

of degree

\geq 1

, show that the mapping

f \to f(h)

is a one-one linear transformation of

F[x]

into

F[x]

. Show that this transformation is an isomorphism of

F[x]

onto

F[x]

if and only if

\deg h = 1