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Linear Algebra - Polar decomposition

  1. Apr 6, 2010 #1
    nwjyoz.jpg

    First i calculated the eigenvalues: I got
    [tex](i-\lambda)(-i-\lambda)+1[/tex], so
    [tex]\lambda_{1,2}=+-\sqrt{2}i[/tex]

    Is it correct to go on on like this:

    [tex]\lambda_{1}a+b=\sqrt{\lambda_{1}}[/tex]
    [tex]\lambda_{2}a+b=\sqrt{\lambda_{2}}[/tex]

    After calculating a and b, we plug it into f(x) = ax+b -->
    [tex]f(A^{*}A)=a(A^{*}A)+bI[/tex]

    Then
    [tex]f(A^{*}A)=\sqrt{A^{*}A}=|A|[/tex] and
    [tex]U=A|A|^{-1}[/tex]

    This way i find U, and i think |A|=P

    So i have the polar decompostion A = UP?!
    Is the way correct?

    Thx
    Mumba

    Edit: A* - Transpose
     
    Last edited: Apr 6, 2010
  2. jcsd
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