vol18_pp352-363. 139KB Jun 04 2011 12:06:03 AM
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that this conjecture is not true in general for matrices with minimal rank equal to three and for matrices of size n n , n 6.. In this paper we prove that this conjecture is true
Neubauer, An inequality for positive-denite matrices with applications to combi- natorial matrices, Linear Algebra Appl. Neubauer
As is well known, the Schur complements of strictly or irreducibly diagonally dom- inant matrices are H − matrices; however, the same is not true of generally diagonally
positive semi-definite nullity of a graph G is the same as the problem of finding the minimum positive semi-definite rank of G.. Without the requirement that the matrices in (1.1)
It is known that for a totally positive (TP) matrix, the eigenvalues are positive and distinct and the eigenvector associated with the smallest eigenvalue is totally nonzero and has
In the context of invertible M-matrices (i.e., when B ≥ 0), condition (ii) of Theorem 4.3 is associated with diagonal dominance of AD because the diagonal entries are positive and
Further, we give some L¨ owner partial orders for compound matrices of Schur complements of positive semidefinite Hermitian matrices, and obtain some estimates for eigenvalues of
For example, in [3], it is shown that a positive semigroup whose diagonal entries are binary (equal to 0 or 1), is either decomposable, or similar, via a positive diagonal
