Some inequalities for sums of nonnegative definite matrices in quaternions.
Some properties of the -adic Vandermonde matrix.
Some remarks on generalized inverses of conjugate EP matrix.
Some remarks on operators preserving partial orders of matrices
Stępniak [Linear Algebra Appl. 151 (1991)] considered the problem of equivalence of the Löwner partial order of nonnegative definite matrices and the Löwner partial order of squares of those matrices. The paper was an important starting point for investigations of the problem of how an order between two matrices A and B from different sets of matrices can be preserved for the squares of the corresponding matrices A² and B², in the sense of the Löwner partial ordering, the star partial ordering,...
Spectral properties of sign symmetric matrices.
Statistically strongly regular matrices and some core theorems.
Structure preserving algorithms for perplectic eigenproblems.
Structured condition numbers and backward errors in scalar product spaces.
Structured conditioning of matrix functions.
Structured Jordan canonical forms for structured matrices that are Hermitian, skew Hermitian or unitary with respect to indefinite inner products.
Structured tools for structured matrices.
Subdirect sums of doubly diagonally dominant matrices.
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).
Sur la transformée de Laplace de considérée comme fonction de la diagonale de
Symmetric nonnegative realization of spectra.
The classification of edges and the change in multiplicity of an eigenvalue of a real symmetric matrix resulting from the change in an edge value
We take as given a real symmetric matrix A, whose graph is a tree T, and the eigenvalues of A, with their multiplicities. Each edge of T may then be classified in one of four categories, based upon the change in multiplicity of a particular eigenvalue, when the edge is removed (i.e. the corresponding entry of A is replaced by 0).We show a necessary and suficient condition for each possible classification of an edge. A special relationship is observed among 2-Parter edges, Parter edges and singly...
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 Eigenvalues and Singular Values of Matrix Sums and Product, VIII: Displacement of Indices
The external vertices conjecture in case .