Before revision:  In this note we analyze in detail how the EIM at each iteration attempts to choose the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy.
After revision:  In this article we clarify a common misperception of the EIM as originally introduced and used in practice in GW science. Namely, we prove that the EIM at each iteration attempts to choose the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy.