In this paper, the author says that if $A$ is an $n\times n$ matrix and $P$ is the transformation such that $P^{-1}AP=J$ where $J=\text{diag}(\lambda_1,\lambda_2, \dots, \lambda_n)$. Then we can define $$G=\{P\mid P^{-1}AP=J\}.$$ Then we say that $\kappa(A)=\min_G||P||_2\ ||P^{-1}||_2$. is called the $\textit{Spectral Condition number of $A$}$
I haven't seen this definition before and I'm curious as to where they got it.