Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Drexel28

Math Help - similar to its transpose

  1. #1
    Newbie
    Joined
    Aug 2013
    From
    Mars
    Posts
    6

    similar to its transpose

    Let N be an k*k nilpotent matrix with nilpotency index k i.e. N^k=0 but N^{k-1} \neq 0 . I want to show that N^t (transpose of N) is similar to N.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21

    Re: similar to its transpose

    I mean, since \mathbb{R} or \mathbb{C} contain all the eigenvalues of N you can conjugate to put it in Jordan canonical form and then you only have to note that the Jordan matrix is similar to its transpose.
    Thanks from Human
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 22nd 2011, 12:12 AM
  2. Transpose of a transpose
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: June 2nd 2011, 02:37 PM
  3. Replies: 13
    Last Post: December 9th 2010, 03:19 PM
  4. help with transpose plz
    Posted in the Algebra Forum
    Replies: 5
    Last Post: April 2nd 2010, 03:10 AM
  5. Prove if B is similar to A then A is similar to B
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 10th 2010, 06:26 PM

Search Tags


/mathhelpforum @mathhelpforum