Linear Algebra - Polar decomposition

  • Thread starter Mumba
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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:

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