## Acalytica

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What is the logarithmic norm?
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Let $A$ be a square matrix and $\|\cdot\|$ be an induced matrix norm. The associated logarithmic norm $\mu$ of $A$ is defined
$\mu(A)=\lim _{h \rightarrow 0^{+}} \frac{\|I+h A\|-1}{h}$
Here $I$ is the identity matrix of the same dimension as $A$, and $h$ is a real, positive number. The limit as $h \rightarrow 0^{-}$equals $-\mu(-A)$, and is in general different from the logarithmic norm $\mu(A)$, as $-\mu(-A) \leq \mu(A)$ for all matrices.
by Diamond (78,219 points)

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