= Decaying bound for symmetric negative matrix splitting
{title2=$\|E(t)\|_2\leq2\|B\|_2(e^{t(a+b)}-e^{tc})/(a+b-c)$}
For symmetric negative-definite <matrices>, put $a=\lambda_{\max}(A)$, $b=\lambda_{\max}(B)$ and $c=\lambda_{\max}(A+B)\leq a+b$. The <spectral theorem> gives exact exponential norm bounds, and $\|[e^{sA},B]\|_2\leq2\|B\|_2e^{sa}$. Integration in the <exponential product defect identity> proves the displayed estimate if $c<a+b$. At equality its continuous limit is $2t\|B\|_2e^{tc}$; the quotient must not be interpreted as division by zero.
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