Some new results on determinantal inequalities and applications.
Some results on eigenvalues of nonnegative matrices
Some results on matrix partial orderings and reverse order law.
Spectra of weighted compound graphs of generalized Bethe trees.
Spectral radius preservers of products of monnegative matrices.
Spectrum preserving lower triangular completions -- the nonnegative nilpotent case.
Subdirect sums of nonsingular -matrices and of their inverses.
Subdirect sums of -strictly diagonally dominant matrices.
Sufficient conditions to be exceptional
A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A is exceptional. We also show that the only 5-by-5 exceptional matrix with a hollow nonnegative inverse is the Horn matrix (up to positive diagonal congruence and permutation similarity).
Symmetric nonnegative realization of spectra.
The 123 theorem of Probability Theory and Copositive Matrices
Alon and Yuster give for independent identically distributed real or vector valued random variables X, Y combinatorially proved estimates of the form Prob(∥X − Y∥ ≤ b) ≤ c Prob(∥X − Y∥ ≤ a). We derive these using copositive matrices instead. By the same method we also give estimates for the real valued case, involving X + Y and X − Y, due to Siegmund-Schultze and von Weizsäcker as generalized by Dong, Li and Li. Furthermore, we formulate a version of the above inequalities as an integral inequality...
The algebraic connectivity of two trees connected by an edge of infinite weight.
The Collatz-Wielandt quotient for pairs of nonnegative operators
In this paper we consider two versions of the Collatz-Wielandt quotient for a pair of nonnegative operators that map a given pointed generating cone in the first space into a given pointed generating cone in the second space. If the two spaces and two cones are identical, and is the identity operator, then one version of this quotient is the spectral radius of . In some applications, as commodity pricing, power control in wireless networks and quantum information theory, one needs to deal with...
The combinatorial structure of eventually nonnegative matrices.
The combinatorially symmetric -matrix completion problem.
The Dittert's function on a set of nonnegative matrices.
The eigenvalue distribution on Schur complement of nonstrictly diagonally dominant matrices and general -matrices.
The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices
In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.
The Frisch scheme in algebraic and dynamic identification problems
This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension...
The general totally positive matrix completion problem with few unspecified entries.