I saw a similar post to this one, but i just got lost in the mess of the whole thing. So i just started a new thread.(adsbygoogle = window.adsbygoogle || []).push({});

A question reads:

Let T: Pn ---> Pn be defined by T[P(x)] = p(x) + xp'(x), where p'(x) denotes the derivative. Show that T is an isomorphism by finding Mbb(T) when B = {1, x, x^2, ... , x^n}

From doing the other question and problems in the text book, i know how to find Mdb(T). I suppose that finding Mbb(T) would be very similar.

I did it like this:

Mbb(T) = [ CbT(1) CbT(x) CbT(x^2) ... CbT(X^n) ]

Mbb(T) = [ Cb(1) Cb(2x) Cb(3x^2) .... Cb((n+1)X^n]

and it gives this nxn matrix:

[1 0 0 ......... 0]

[0 2 0 ......... 0]

[0 0 3 ......... 0]

[0 0 0 ... (n+1)]

now, an isomorphism means that the linear transformation is both one-to-one and onto.

How do you tell that its an isomorphism by just looking at the matrix?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: The Matrix Of A Linear Transformation

**Physics Forums | Science Articles, Homework Help, Discussion**