Spectral abscissa ($s(A)={\max }_{\lambda \in \sigma (A)}\mathrm{Re}\lambda$)

The spectral abscissa is the largest real part of a matrix's eigenvalues. It describes asymptotic exponential rates of its matrix exponential, but a non-normal matrix can also have transient amplification. It is generally distinct from the Euclidean logarithmic norm, which gives an immediate Euclidean energy-growth bound.