ON THE FACIAL STRUCTURE OF THE SET OF CORRELATION-MATRICES

Authors
LAURENT M POLJAK S
Citation
M. Laurent et S. Poljak, ON THE FACIAL STRUCTURE OF THE SET OF CORRELATION-MATRICES, SIAM journal on matrix analysis and applications, 17(3), 1996, pp. 530-547
Citations number
20
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on matrix analysis and applications → ACNP
ISSN journal
08954798
Volume
17
Issue
3
Year of publication
1996
Pages
530 - 547
Database
ISI
SICI code
0895-4798(1996)17:3<530:OTFSOT>2.0.ZU;2-4
Abstract
We study the facial structure of the set E(nxn) of correlation matrice s (i.e., the positive semidefinite matrices with diagonal entries equa l to I). In particular, we determine the possible dimensions for a fac e, as well as for a polyhedral face, of E(nxn). It turns out that the spectrum of face dimensions is lacunary and that E(nxn) has polyhedral faces of dimension up to approximate to root 2n. As an application, w e describe in detail the faces of E(4x4) We also discuss results relat ed to optimization over E(nxn).