1. Limited time only! Sign up for a free 30min personal 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!

If M is diagonalizable, find a matrix N^3 = M

  1. May 15, 2014 #1
    I have a question about diagonalizable matrix

    So now I have showed M is a diagonalizable and I am asked to find a matrix N^3=M

    Obviously if M=PDP^(-1)
    then N=PD^(1/3)P^(-1) but I am wondering how to show it formally.
     
  2. jcsd
  3. May 15, 2014 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Given that ##N=PD^{1/3}P^{-1}##, what is ##N^3=NNN##?
     
  4. May 15, 2014 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Strictly speaking, also need to show that this generates all solutions of the original equation.
     
  5. May 16, 2014 #4

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    I'm not sure what you mean by that. Per the title of the thread, victoranderson has to find a matrix N such that N^3=M, not all matrices N such that N^3=M.

    What he does need to show is that his D^(1/3) always exists and that (D^(1/3))^3=D.
     
  6. May 16, 2014 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    True.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted