Further remarks on the Cayley-Hamilton theorem and Leverrier's method for the matrix pencil (sE - A)

Some results for matrix pencils are extended to the singular case (sE - A) . A singular Leverrier's relation, Cayley-Hamilton theorem, and Newton's formula are given. A finite-series expansion for (sE - A)^{-1} is given in terms of the generalized Tschirnhausen polynomials.