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 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...
متن کاملThe N 10 - Matrix Completion Problem
An n×n matrix is called an N1 0 -matrix if all its principal minors are non-positive and each entry is non-positive. In this paper, we study general combinatorially symmetric partial N1 0 -matrix completion problems and prove that a combinatorially symmetric partial N1 0 -matrix with all specified offdiagonal entries negative has an N1 0 -matrix completion if the graph of its specified entries ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.07.020