# Linear Algebra - Polar decomposition

1. Apr 6, 2010

### Mumba

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

Is it correct to go on on like this:

$$\lambda_{1}a+b=\sqrt{\lambda_{1}}$$
$$\lambda_{2}a+b=\sqrt{\lambda_{2}}$$

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

Then
$$f(A^{*}A)=\sqrt{A^{*}A}=|A|$$ and
$$U=A|A|^{-1}$$

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