THE GROUP INVERSE OF THE TRANSFORMATION S(X)=AX-XB

Authors
HEINIG G
Citation
G. Heinig, THE GROUP INVERSE OF THE TRANSFORMATION S(X)=AX-XB, Linear algebra and its applications, 257, 1997, pp. 321-342
Citations number
14
Categorie Soggetti
Mathematics,Mathematics
Journal title
Linear algebra and its applications → ACNP
ISSN journal
00243795
Volume
257
Year of publication
1997
Pages
321 - 342
Database
ISI
SICI code
0024-3795(1997)257:<321:TGIOTT>2.0.ZU;2-P
Abstract
The group inverse L# of the Sylvester transformation L(X) = AX - XB is (provided that it exists) represented in polynomial form L#(Y) = Sigm a(ij)c(ij)A(i)YB(j) in terms of the minimal polynomials of A and B. In one of the representations the coefficient matrix [c(ij)] is expresse d with the help of a new class of ''derived'' Hankel matrices. (C) Els evier Science Inc., 1997.