1996
On the facial structure of the set of correlation matrices
Publication
Publication
SIAM Journal on Matrix Analysis and Applications , Volume 17 p. 530- 547
We study the facial structure of the set ${cal E_{ntimes n$ of correlation matrices (i.e., the positive semidefinite matrices with diagonal entries equal to 1). In particular, we determine the possible dimensions for a face, as well as for a polyhedral face of ${cal E_{ntimes n$. It turns out that the spectrum of face dimensions is lacunary and that ${cal E_{ntimes n$ has polyhedral faces of dimension up to $approx sqrt {2n$. As an application, we describe in detail the faces of ${cal E_{4times 4$. We also discuss results related to optimization over ${cal E_{ntimes n$.
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S.I.A.M. | |
SIAM Journal on Matrix Analysis and Applications | |
Laurent, M., & Poljak, S. (1996). On the facial structure of the set of correlation matrices. SIAM Journal on Matrix Analysis and Applications, 17, 530–547. |