Science:Math Exam Resources/Courses/MATH307/December 2008/Question 09
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Question 09 |
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Find the singular values of Then determine the diagonal matrix in the singular value decomposition A =. |
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? |
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. |
Hint 1 |
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The singular values of A are the square root of the eigenvalues of ATA. |
Hint 2 |
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The matrix Σ has the same dimension as A and holds the singular values on the diagonal. |
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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Solution |
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Please rate my easiness! It's quick and helps everyone guide their studies. Given and we calculate , which has the eigenvalues 2 and 1. Hence, the singular values of A are and . Putting the singular values on the diagonal of Σ we find that |