ELA, Volume 7, pp. 182-190, December 2000, abstract
Separable characteristic polynomials of pencils and property L
John Maroulas, Panayiotis J. Psarrakos, and Michael J. Tsatsomeros
The condition (SC): det(I-sA-tB) = det(I-sA) det(I-tB) for all
scalars s,t, has naturally and long been connected to eigenvalue
properties of the matrix pair A,B. In particular, Taussky used the
notion of property L to generalize the Craig-Sakamoto Theorem by
showing that when A and B are normal, (SC) is equivalent to AB=0.
The relation of (SC) to the eigenspaces of A, B and sA+tB is examined
in order to obtain necessary and/or sufficient conditions in terms
of eigenspaces and space decompositions. A general criterion for (SC)
based on the spectrum of the n by n matrix polynomial
lambda^{2n+1} I - lambda^{2n} A - B is also presented.