Science:Math Exam Resources/Courses/MATH307/April 2010/Question 05 (b)/Solution 1

From (a) we found that U is unitary. With this definition,

$U S V^{*} = A V S^{- 1} S V^{*} = A$ .

Then,

$U S^{2} U^{*} = A V S^{- 1} S^{2} S^{- 1} V^{*} A^{*} = A A^{*}$

From this, we can see that U diagonalizes $A A^{*}$