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Linear algebra again

  1. Mar 23, 2006 #1
    Consider the equation x^2 + xy + y^2 = 1. Find a rotation so that the equation has no cross term.

    here a=b=c=1 right
    but how do i find an angle by which to rotate???
    the text says the angle is pi/4... i dont know how they got that .. though
     
  2. jcsd
  3. Mar 23, 2006 #2

    Galileo

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    Start by writing it as a matrix equation:

    [tex]x^2+xy+y^2=\vec x^T A \vec x[/tex]
     
  4. Mar 23, 2006 #3

    HallsofIvy

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    Once you have the A Galileo is talking about, find its eigenvalues and eigenvectors. The eigenvectors give the directions for the new axes.
     
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