Maroulas, John; Psarrakos, Panayiotis J.; Tsatsomeros, Michael J.

Separable characteristic polynomials of pencils and property $L$

Electron. J. Linear Algebra 7, 182-190, electronic only (2000)

Summary

Summary: The condition (SC): $det(I \Gamma sA\Gamma tB) = det(I \Gamma sA) det(I \Gamma tB)$ 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 suAEcient conditions in terms of eigenspaces and space decompositions. A general criterion for (SC) based on the spectrum of the n $\Theta n$ matrix polynomial * 2n+1 I $\Gamma * 2n$ A $\Gamma B$ is also presented.

Mathematics Subject Classification

15A15, 15A18, 15A22

Keywords/Phrases

characteristic polynomial, property L, craig-sakamoto theorem, matrix polynomial

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