1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Characteristic polynomial and polynomial vector space

  1. Apr 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Let [tex] V:= ℝ_{2}[t] [/tex]
    [tex]V \in f: v \mapsto f(v) \in V, \forall v \in V (f(v))(t) := v(2-t)[/tex]
    a) Check that [tex] f \in End(V) [/tex]
    b) Calculate the characteristic polynomial of f.
    2. Relevant equations

    3. The attempt at a solution
    a) Is it sufficient to check that [tex](f+g)(t)=f(t)+g(t)[/tex] ?
    b) Standard basis of polynomials is [tex]1+t+t^2[/tex], so [tex] f(1)=(2-t) \\ f(t)=2t - t^2 \\ f(t^2)=2t^2-t^3[/tex]

    What should I do next? What's up with [tex]t^3[/tex] ? (The space is of polynomials of degree at most 2). How do I calculate this map into a matrix ?
     
  2. jcsd
  3. Apr 13, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Well, as you've observed, the given map doesn't take second degree polynomial into second degree polynomials, it maps them into the space of third degree polynomials. That wouldn't stop you from writing a matrix for it, but it won't be square. Not sure what to do with the rest of the question at all.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Characteristic polynomial and polynomial vector space
  1. Polynomial Vector Spaces (Replies: 11)

Loading...