Results 1 to 2 of 2

Math Help - Complex eigenvalues/eigenvectors

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    48

    Complex eigenvalues/eigenvectors

    Given the rotation matrix (cos x -sin x)
    sinx cosx
    (supposed to by a 2x2 matrix)

    I have to find the complex eigenvalues and eigenvectors when sin x not=0

    Dont know if i'm going the right way but I have p(L) = det(cosx-L -sin x)
    sin x cosx-L

    = (cosx-L)^2 - (-sinx)^2 = (cosx)^2-2Lcosx+L^2+(sinx)^2

    =L^2-2Lcosx+1

    I dont know where to go from here, thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by jpquinn91 View Post
    Given the rotation matrix (cos x -sin x)
    sinx cosx
    (supposed to by a 2x2 matrix)

    I have to find the complex eigenvalues and eigenvectors when sin x not=0

    Dont know if i'm going the right way but I have p(L) = det(cosx-L -sin x)
    sin x cosx-L

    = (cosx-L)^2 - (-sinx)^2 = (cosx)^2-2Lcosx+L^2+(sinx)^2

    =L^2-2Lcosx+1

    I dont know where to go from here, thanks


    Weird choice for the polynomial's unknown...L...perhaps trying to make it similar to \lambda ? Anyway, evaluate the quadratic's discriminant:

    \Delta =4\cos^2x-4=4(\cos^2x-1)=-4\sin^2x , so the (necessarily complex non-real...why?) roots are \frac {2\cos x\pm 2\sin x\,i}{2}=\cos x \pm i\sin x =e^{\pm ix} .

    Take it from here now.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. eigenvectors/eigenvalues
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 20th 2011, 11:38 AM
  2. Eigenvectors and eigenvalues.
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 28th 2010, 08:52 PM
  3. Eigenvalues and Eigenvectors
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 1st 2010, 10:41 PM
  4. Eigenvalues and Eigenvectors
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: November 16th 2009, 06:00 AM
  5. Eigenvalues and Eigenvectors
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 21st 2008, 11:01 PM

Search Tags


/mathhelpforum @mathhelpforum