The Cayley–Menger determinant is irreducible for .
The Chebyshev Solution of Certain Matrix Equations.
The Chebyshev Solution of the Linear Matrix Equation AX + YB = C.
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 classification of Lie algebras with invariant cones.
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 comparison of spectrum of normalizable matrices
The compression semigroup of a cone is connected.
The convergence of a new method for calculating lower bounds to eigenvalues
The convex analysis of unitarily invariant matrix functions.
The Coordinex Problem and Its Relation to the Conjecture of Wilkinson.
The critical exponent of operators with constrained spectral radius
The -stability problem for real matrices
We give detailed discussion of a procedure for determining the robust -stability of a real matrix. The procedure begins from the Hurwitz stability criterion. The procedure is applied to two numerical examples.
The determinant concept defined by means of graph theory
The Direct and Inverse Spectral Problems for some Banded Matrices
2000 Mathematics Subject Classification: 15A29.In this paper we introduced a notion of the generalized spectral function for a matrix J = (gk,l)k,l = 0 Ґ, gk,l О C, such that gk,l = 0, if |k-l | > N; gk,k+N = 1, and gk,k-N № 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.
The distance matrix of a bidirected tree.
The distribution of eigenvalues of randomized permutation matrices
In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter ) by replacing the entries equal to one by more general non-vanishing complex random variables. For these ensembles, in contrast with more classical models as the Gaussian Unitary Ensemble, or the Circular Unitary Ensemble, the eigenvalues can be very explicitly computed by using the cycle structure of the permutations....
The Dittert's function on a set of nonnegative matrices.