Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $T:V \longrightarrow V$ a linear operator, where $V$ is a vector space over the field $\mathbb{K}$. Show that if $p(x),q(x)\in \mathcal{P}(\mathbb{K})$, then

$$(p\cdot q)(T)(v)=p(q(T))(v), \ \ \forall v\in V.$$

I have some examples but I get no such equality. I am taking $p \cdot q $ as the product of polynomials, as in the book i'm following do not indicate the meaning of that product. Could anyone help me or give me some pointers?

share|cite|improve this question

You might already know this, but as indicated by $p(q(T))$, $p\cdot q$ is related to a Function composition of $q$ and $p$:

First apply $q$ on $x$, then $p$ on $q(T)$, so to me, this looks just like a definition.

But, it's also true in a multiplicative sense, if $p(x)$ or $q(x)$ is constant :-).

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.