More precisely, if A is a complex matrix, then what are the singular values of A+zI where z is a complex number and I is the identity matrix ?
You will find the response to this question in here, where a very intuitive proof is used:
https://www.quora.com/How-does-adding-some-multiple-of-the-identity-change-the-singular-Values-of-a-Matrix
|| A+zI ||
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