= Euclidean logarithmic norm
{c}
{title2=$\mu_2(A)=\lambda_{\max}((A+A^*)/2)$}
= Numerical abscissa
{synonym}
= Euclidean matrix measure
{c}
{synonym}
The <Euclidean logarithmic norm> is the largest <eigenvalue> of a <matrix>'s Hermitian part. Differentiating $\|y\|_2^2$ along $y'=Ay$ gives $\|e^{tA}\|_2\leq e^{t\mu_2(A)}$. It is the least exponent for such a bound with prefactor one, as a first-order expansion at zero shows. It equals the <spectral abscissa> for a <normal matrix>, but need not do so otherwise. A scalar rational <stability function> does not generally inherit a bound by its value at this real number.
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