Geodesic
The $Q$-matrix completion problem
The electronic journal of linear algebra, Tome 18 (2009), pp. 176-191.

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

Summary: A real n $\times n$ matrix is a Q-matrix if for every k = 1, 2, . . . , n the sum of all k $\times k$ principal minors is positive. A digraph D is said to have Q-completion if every partial Q-matrix specifying D can be completed to a Q-matrix. For the Q-completion problem, sufficient conditions for a digraph to have Q-completion are given, necessary conditions for a digraph to have Q-completion are provided, and those digraphs of order at most four that have Q-completion are characterized.
Classification : 15A48, 05C50
Keywords: partial matrix, matrix completion, Q-matrix, Q-completion, digraph 
@article{ELA_2009__18__a43,
     author = {Dealba, Luz Maria and Hogben, Leslie and Sarma, Bhaba Kumar},
     title = {The $Q$-matrix completion problem},
     journal = {The electronic journal of linear algebra},
     pages = {176--191},
     publisher = {mathdoc},
     volume = {18},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2009__18__a43/}
}
TY  - JOUR
AU  - Dealba, Luz Maria
AU  - Hogben, Leslie
AU  - Sarma, Bhaba Kumar
TI  - The $Q$-matrix completion problem
JO  - The electronic journal of linear algebra
PY  - 2009
SP  - 176
EP  - 191
VL  - 18
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ELA_2009__18__a43/
LA  - en
ID  - ELA_2009__18__a43
ER  - 
%0 Journal Article
%A Dealba, Luz Maria
%A Hogben, Leslie
%A Sarma, Bhaba Kumar
%T The $Q$-matrix completion problem
%J The electronic journal of linear algebra
%D 2009
%P 176-191
%V 18
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ELA_2009__18__a43/
%G en
%F ELA_2009__18__a43
Dealba, Luz Maria; Hogben, Leslie; Sarma, Bhaba Kumar. The $Q$-matrix completion problem. The electronic journal of linear algebra, Tome 18 (2009), pp. 176-191. http://geodesic.mathdoc.fr/item/ELA_2009__18__a43/