I need help finding the polar

decomposition

of

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- Dec 12th 2009, 07:25 PMmancillaj3finding polar decomposition!
I need help finding the polar

decomposition

of

- Dec 14th 2009, 12:51 PMOpalg
If then the polar decomposition of A is a factorisation , where U is unitary and R is positive. To find R use the fact that . So R is the positive square root of that matrix, which you can compute by diagonalising it. You should find that the eigenvalues of are 50 and 200, with corresponding normalised eigenvectors and . So , where and . The square root is given by , where .

Having found R, you can then get U as .