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Trace inequality

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Hi there,

I'm having trouble understanding a step in a textbook I'm currently reading (MIT Lectures on Dynamic Systems and Control); I just took a picture of the text to save myself the trouble of copying it over. W is a unitary matrix, [math]\sigma_i[/math] are the singular values of A.




I haven't the slightest clue as to why this might be, and seeing as I've search the internet and found no refference to this and the author's don't elaborate I assume it's fairly simple and should be well within my reach, but for some reason I just don't get it. Thanks in advance for any help.

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