I need help finding the polar
decomposition
of
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 .