As a lead- in to the SVD , we discussed the polar decomposition of a square nonsingular matrix . Here is a reminder :

As a lead- in to the SVD , we discussed the polar decomposition of a square nonsingularmatrix . Here is a reminder : if A is nixon , its polar decomposition is A = QE whereQ is an orthogonal matrix and E is a positive definite symmetric matrix ( which mustevidently satisfy 2 - AT A )( a ) Show that from the singular value decomposition of A you can easily obtain thepolar decomposition of A , and vice versa( b ) The polar decomposition can be found directly by ( 1 ) diagonalizing ATA , iewriting it as RDRT with R orthogonal ; ( i ) taking E - RV DRY ; ( i ) takingQ - AF - 1 Implement this for the 2 x 2 matrix5 3