The (weakly) sign symmetric P-matrix completion problems

Matrix Completion Problems

Matrix completion problems are concerned with determining whether partially speciied matrices can be completed to fully speciied matrices satisfying certain prescribed properties. In this article we survey some results and provide references about these problems for the following matrix properties: positive semideenite matrices, Euclidean distance matrices, completely positive matrices, contrac...

Deterministic Symmetric Positive Semidefinite Matrix Completion

We consider the problem of recovering a symmetric, positive semidefinite (SPSD) matrix from a subset of its entries, possibly corrupted by noise. In contrast to previous matrix recovery work, we drop the assumption of a random sampling of entries in favor of a deterministic sampling of principal submatrices of the matrix. We develop a set of sufficient conditions for the recovery of a SPSD matr...

Euclidean distance matrix completion problems

A Euclidean distance matrix is one in which the (i, j) entry specifies the squared distance between particle i and particle j. Given a partially-specified symmetric matrix A with zero diagonal, the Euclidean distance matrix completion problem (EDMCP) is to determine the unspecified entries to make A a Euclidean distance matrix. We survey three different approaches to solving the EDMCP.We advoca...

The partial non - combinatorially symmetric N 10 - matrix completion problem

An n×n matrix is called an N 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N 0 -completion. Therefore, we have given sufficient conditions ...

Sign Wave Analysis in Matrix Eigenvalue Problems