A note on Homotopic Deviation versus perturbation

This short note presents a simple algebraic result about matrices and associated polynomials which clarifies a central point in the Homotopic Deviation theory presented in chapter 7 of [3], . The polynomial is defined by Chatelin in [3], . The polynomial is used by Lidskii in [11,13], and by Chatelin in [3]. In this note we prove that these two polynomials are equal up to a nonzero constant.