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- Thread starter Abbas
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Thanks, but Are you sure if this is true?Welcome to MHB, Abbas!

\begin{aligned}

\text{cond}(A+B)

&= ||(A+B)^{-1}|| \cdot ||A+B|| \\

&= ||A^{-1} + B^{-1}||\cdot ||A+B|| \\

&\le \Big(||A^{-1}||+||B^{-1}||\Big) \cdot \Big(||A||+||B||\Big) \\

&\le ||A^{-1}||\cdot||A|| + ||B^{-1}||\cdot||B|| \\

&= \text{cond}(A) + \text{cond}(B)

\end{aligned}

I doubt (A+B)

How about ||A

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- Mar 5, 2012

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You're quite right. I had just deleted my post, since I realized it was not correct due to the very reasons you mention.Thanks, but Are you sure if this is true?

I doubt (A+B)^{-1}= A^{-1}+B^{-1}.

How about ||A^{-1}||⋅||B||+||A||⋅||B^{-1}|| ? can these terms be omitted?

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I was looking for an answer since I post it here, cond(A+B) =< cond(A) + cond(B) is not always true. the hypothesis is wrong. Thanks BTW.You're quite right. I had just deleted my post, since I realized it was not correct due to the very reasons you mention.