Related papers: Matrix completion and semidefinite matrices

The main goal of this article is to study the existence of a unique positive definite common solution to a pair of matrix equations of the form \begin{eqnarray*} X^r=Q_1 + \displaystyle \sum_{i=1}^{m} {A_i}^*F(X)A_i \mbox{ and } X^s=Q_2 +…

In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.

A real symmetric n times n matrix is called copositive if the corresponding quadratic form is non-negative on the closed first orthant. If the matrix fails to be copositive there exists some non-negative certificate for which the quadratic…

Consider a matrix function f defined for Hermitian matrices. The purpose of this paper is two-fold. We derive new results for the absolute structured condition number of the matrix function and we derive new bounds for the perturbation…

Consider a convex set S defined by a matrix inequality of polynomials or rational functions over a domain. The set S is called semidefinite programming (SDP) representable or just semidefinite representable if it equals the projection of a…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

The main aim of this paper is to characterize ideals I in the power series ring R=K[[x1,...,xs]] that are finitely determined up to contact equivalence by proving that this is the case if and only if I is an isolated complete intersection…

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…

We present randomized algorithms for estimating the trace and deter- minant of Hermitian positive semi-definite matrices. The algorithms are based on subspace iteration, and access the matrix only through matrix vector products. We analyse…

Canonical matrices of (a) bilinear and sesquilinear forms, (b) pairs of forms, in which every form is symmetric or skew-symmetric, and (c) pairs of Hermitian forms are given over finite fields of characteristic not 2 and over finite…

This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.

A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite. Motivated by the fact that diagonal LMIs define polyhedra, the solution set…

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We…

Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…

The problem of matrix completion and decomposition in the cone of positive semidefinite (PSD) matrices is a well-understood problem, with many important applications in areas such as linear algebra, optimization, and control theory. This…

We prove that the only entrywise transforms of rectangular matrices which preserve total positivity or total non-negativity are either constant or linear. This follows from an extended classification of preservers of these two properties…

We describe a way to complete a correlation matrix that is not fully specified. Such matrices often arise in financial applications when the number of stochastic variables becomes large or when several smaller models are combined in a…

We characterize the existence of a polynomial (rational) matrix when its eigenstructure (complete structural data) and some of its rows are prescribed. For polynomial matrices, this problem was solved in a previous work when the polynomial…

Let $\mathbb{N}$ be a set of the natural numbers. Symmetric inverse semigroup $R_\infty$ is the semigroup of all infinite 0-1 matrices $[g_{ij}]$ with at most one 1 in each row and each column such that $g_{ii}=1$ on the complement of a…

For a domain $G$ in the one-point compactification $\overline{\mathbb{R}}^n = \mathbb{R}^n \cup \{ \infty\}$ of $\mathbb{R}^n, n \ge 2$, we characterize the completeness of the modulus metric $\mu_G$ in terms of a potential-theoretic…