Geodesic
Constructing copositive matrices from interior matrices
The electronic journal of linear algebra, Tome 17 (2008), pp. 9-20.

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

Summary: Let A be an n by n symmetric matrix with real entries. Using the l 1 -norm for vectors and letting S + 1 = x $\in R$ n |||x|| 1 = 1 , x $\geq 0$, the matrix A is said to be interior if the quadratic form x T Ax achieves its minimum on S + 1 in the interior. Necessary and sufficient conditions are provided for a matrix to be interior. A copositive matrix is referred to as being exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. A method is provided for constructing exceptional copositive matrices by completing a partial copositive matrix that has certain specified overlapping copositive interior principal submatrices.
Classification : 15A18, 15A48, 15A57, 15A63
Keywords: copositive matrix, interior matrix, quadratic form, almost positive semidefinite, exceptional copositive matrix, extreme copositive matrix 
@article{ELA_2008__17__a43,
     author = {Johnson, Charles R. and Reams, Robert},
     title = {Constructing copositive matrices from interior matrices},
     journal = {The electronic journal of linear algebra},
     pages = {9--20},
     publisher = {mathdoc},
     volume = {17},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2008__17__a43/}
}
TY  - JOUR
AU  - Johnson, Charles R.
AU  - Reams, Robert
TI  - Constructing copositive matrices from interior matrices
JO  - The electronic journal of linear algebra
PY  - 2008
SP  - 9
EP  - 20
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ELA_2008__17__a43/
LA  - en
ID  - ELA_2008__17__a43
ER  - 
%0 Journal Article
%A Johnson, Charles R.
%A Reams, Robert
%T Constructing copositive matrices from interior matrices
%J The electronic journal of linear algebra
%D 2008
%P 9-20
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ELA_2008__17__a43/
%G en
%F ELA_2008__17__a43
Johnson, Charles R.; Reams, Robert. Constructing copositive matrices from interior matrices. The electronic journal of linear algebra, Tome 17 (2008), pp. 9-20. http://geodesic.mathdoc.fr/item/ELA_2008__17__a43/