Geodesic
$Z$-pencils
The electronic journal of linear algebra, Tome 4 (1998), pp. 32-38.

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

Summary: The matrix pencil (A; B) = ftB $\Gamma A$ j t 2 C g is considered under the assumptions that A is entrywise nonnegative and B $\Gamma A$ is a nonsingular M-matrix. As t varies in [0; 1], the Z-matrices tB $\Gamma A$ are partitioned into the sets L s introduced by Fiedler and Markham. As no combinatorial structure of B is assumed here, this partition generalizes some of their work where B = I. Based on the union of the directed graphs of A and B, the combinatorial structure of nonnegative eigenvectors associated with the largest eigenvalue of (A; B) in [0; 1) is considered.
Classification : 15A22, 15A48, 05C50
Keywords: Z-matrix, matrix pencil, M-matrix, eigenspace, reduced graph 
@article{ELA_1998__4__a2,
     author = {McDonald, Judith J. and Olesky, D.Dale and Schneider, Hans and Tsatsomeros, Michael J. and van den Driessche, P.},
     title = {$Z$-pencils},
     journal = {The electronic journal of linear algebra},
     pages = {32--38},
     publisher = {mathdoc},
     volume = {4},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_1998__4__a2/}
}
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McDonald, Judith J.; Olesky, D.Dale; Schneider, Hans; Tsatsomeros, Michael J.; van den Driessche, P. $Z$-pencils. The electronic journal of linear algebra, Tome 4 (1998), pp. 32-38. http://geodesic.mathdoc.fr/item/ELA_1998__4__a2/