Results 1 to 2 of 2

Thread: Differentiation Operator

  1. #1
    Apr 2013

    Differentiation Operator

    Let D : R3[x] -> R3[x] be the di erentiation operator. Does there exist a basis of R3[x] with respect to
    which the matrix representation of D is:

    This is part of our review for my Linear Algebra class. How do I go about finding a basis (if there is one) for D to be diagonalizable and symmetric?

    Before you ask, no this is not homework. It is questions my teacher made up for the exam and decided to not use so he gave it to us as a study guide.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Apr 2005

    Re: Differentiation Operator

    Have you tried doing any calculations at all? What is " R≤3[x] "? What do derivatives of those functions look like?

    If you tried the simpler example, derivative operator on linear functions, any such function would be of the form y= ax+ b and its derivative would be dy/dx= a. A standard basis would be $\displaystyle v_1= x$ and $\displaystyle v_2= 1$ so that $\displaystyle ax+ b= av_1+ bv_2$ and the derivative would be $\displaystyle a[v_2]$. Using that basis, the matrix representation would be $\displaystyle \begin{bmatrix}0 & 0 \\ a & 0\end{bmatrix}$. Can that be diagonalized or orthogonalized.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. differentiation operator basis
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Apr 2nd 2010, 04:23 AM
  2. Operator in R^n
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Jan 21st 2010, 08:22 AM
  3. D Operator
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: Sep 15th 2009, 11:54 AM
  4. Replies: 3
    Last Post: Aug 14th 2008, 04:03 AM
  5. The use of an operator
    Posted in the Algebra Forum
    Replies: 5
    Last Post: Mar 20th 2008, 01:47 PM

Search tags for this page

Click on a term to search for related topics.

Search Tags

/mathhelpforum @mathhelpforum