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.