Science:Math Exam Resources/Courses/MATH307/April 2013/Question Section 201 07 (c)
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Question Section 201 07 (c) 

Suppose that the matrix A has the following singular value decomposition: where . (c) What are the eigenvalues and eigenvectors of A*A and AA*? 
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Hint 

Science:Math Exam Resources/Courses/MATH307/April 2013/Question Section 201 07 (c)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The eigenvalues and eigenvectors for :
Since ,
Which means that our eigenvalues are , and and the eigenvectors are the columns of V. The eigenvalues and eigenvectors for :
From this equation, we can see that our eigenvalues are the same as the last. However, the corresponding eigenvectors are now the columns of U. 