Results 1 to 6 of 6

Math Help - cayley hamilton theorem problem...

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    15

    Post cayley hamilton theorem problem...

    Hello I have a small problem and I am wondering if someone could help me with Cayley Hamilton Theorem..please!

    Let D = [4 0 0, 0 -1 0, 0 0 9]. Find a matrix D^1/2 E M(3x3) (C) such that

    D^1/2 * D^1/2 = D...

    I know we have to use this product....

    A = VDV^-1....and A^k = VD^kv-1....for example A^2 = VD^2V^-1...

    But I cant take the square root of the D and its elements because it contains -1 as one of its elements...

    please help me!

    thanks a lot!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    This could be really bone-headed, but doesn't



    work? It's a bit hard to read your syntax (MathGuru will hopefully fix LaTeX soon!), but this matrix is definitely in the space of 3 x 3 matrices over the complexes, which is what it looks like your space is.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,282
    Thanks
    673
    i prefer √D =

    [-2 0 0]
    [ 0 -i 0]
    [0 0 -3] and you can't make me change my mind.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Or I suppose you could do any one of the eight possible solutions, right? I don't know of any others.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,282
    Thanks
    673
    one hopes that is why the author of the book in which the problem presumably occurs said "a" matrix, instead of "the" matrix (take the blue pill...)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    May 2010
    Posts
    15
    sir! thanks for the response but I still dont get how you ended up getting that matrix....using cayley hamilton matrix??
    could you please show me the description please?

    thanks a lot!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. cayley-Hamilton law
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 1st 2011, 06:30 AM
  2. Cayley Hamilton Theorem
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: September 6th 2011, 08:32 AM
  3. Cayley Hamilton Theorem Question
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: October 17th 2010, 01:29 PM
  4. Replies: 1
    Last Post: April 6th 2010, 05:42 AM
  5. Cayley-Hamilton Theorem for matrices
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 5th 2009, 07:31 PM

Search Tags


/mathhelpforum @mathhelpforum