Geodesic
Separable characteristic polynomials of pencils and property $L$
The electronic journal of linear algebra, Tome 7 (2000), pp. 182-190.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 15A15, 15A18, 15A22
Keywords: characteristic polynomial, property L, craig-sakamoto theorem, matrix polynomial 
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     author = {Maroulas, John and Psarrakos, Panayiotis J. and Tsatsomeros, Michael J.},
     title = {Separable characteristic polynomials of pencils and property $L$},
     journal = {The electronic journal of linear algebra},
     pages = {182--190},
     publisher = {mathdoc},
     volume = {7},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2000__7__a0/}
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Maroulas, John; Psarrakos, Panayiotis J.; Tsatsomeros, Michael J. Separable characteristic polynomials of pencils and property $L$. The electronic journal of linear algebra, Tome 7 (2000), pp. 182-190. http://geodesic.mathdoc.fr/item/ELA_2000__7__a0/