منابع مشابه
The Q-matrix completion problem
Abstract. A real n × n matrix is a Q-matrix if for every k = 1, 2, . . . , n the sum of all k × k principal minors is positive. A digraph D is said to have Q-completion if every partial Q-matrix specifying D can be completed to a Q-matrix. For the Q-completion problem, sufficient conditions for a digraph to have Q-completion are given, necessary conditions for a digraph to have Q-completion are...
متن کاملThe nonnegative Q − matrix completion problem
In this paper, the nonnegative Q-matrix completion problem is studied. A real n × n matrix is a Q-matrix if for k ∈ {1, . . . , n}, the sum of all k × k principal minors is positive. A digraph D is said to have nonnegative Q-completion if every partial nonnegative Q-matrix specifying D can be completed to a nonnegative Q-matrix. For nonnegative Q-completion problem, necessary conditions and suf...
متن کاملThe Nonsingular Matrix Completion Problem
An n × n matrix is called a principally nonsingular matrix (NSmatrix) if all its principal minors are different from zero and it is called a totally nonsingular matrix (TNS-matrix) if all its minors are different from zero. In this paper, we are interested in the NS-matrix (TNSmatrix) completion problem: whether a partial NS-matrix (TNS-matrix) has a NS-matrix (TNS-matrix) completion. Here, we ...
متن کاملThe CP-Matrix Completion Problem
A symmetric matrix A is completely positive (CP) if there exists an entrywise nonnegative matrix B such that A = BB . We characterize the interior of the CP cone. We formulate the problem as linear optimizations with cones of moments. A semidefinite algorithm is proposed for checking interiors of the CP cone, and its properties are studied. A CP-decomposition of a matrix in Dickinson’s form can...
متن کاملA Survey on the Matrix Completion Problem
Completion problems arise in a variety of applications, such as statistics (e.g. entropy methods for missing data), chemistry (the molecular conformation problem), systems theory, discrete optimization (relaxation methods), data compression, etc., as well as in operator theory and within matrix theory (e.g. determinantal inequalities). In addition to applications, completion problems have provi...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2009
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1303