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CMPE482-Spring2017-Bogazici / hw3

Exercises 3.6.a, 4.5, 5.3
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Problem 4.5 #2

Open yhkalayci opened 7 years ago

yhkalayci commented 7 years ago

Hi,

Do we need to prove the uniqueness of SVD in problem 4.5 or just existance?

mehmetburakkurutmaz commented 7 years ago

We have proven the fact that SVD exists for a general matrix A and under certain conditions it is also unique up to complex signs (in Thm. 4.1). So, if you decompose A, it will definitely have A = USV* form; but you may (possibly) find complex U and V.

To answer your question: You can assume Thm 4.1 without proving. So, you should prove "if A is real, then we can find an U,V couple such that all U{i,j}, V{k,l} are real." and this corresponds to just an existence proof. (Uniqueness proof in Thm. 4.1. under certain conditions will automatically apply)