Given $A, A+E$ nonsingular and $Z=(A+E)^{-1}$. Show $||AZ-I||_2\leq ||E||_2||Z||_2$
Attempt at proof: $||AZ-I||_2=||A(A+E)^{-1}-I||_2\leq ||A(A+E)^{-1}||_2+||I||_2$
I'm not sure how to go about this from this point.
2026-04-23 05:17:04.1776921424
Given $A, A+E$ nonsingular and $Z=(A+E)^{-1}$. Show $||AZ-I||_2\leq ||E||_2||Z||_2$
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Hint
$$ \|AZ-I\|_2=\|AZ-(A+E)Z\|_2 $$