The structured distance to normality of an irreducible real tridiagonal matrix.
The theory and applications of complex matrix scalings
We generalize the theory of positive diagonal scalings of real positive definite matrices to complex diagonal scalings of complex positive definite matrices. A matrix A is a diagonal scaling of a positive definite matrix M if there exists an invertible complex diagonal matrix D such that A = D*MD and where every row and every column of A sums to one. We look at some of the key properties of complex diagonal scalings and we conjecture that every n by n positive definite matrix has at most 2n−1 scalings...
The third smallest eigenvalue of the Laplacian matrix.
The weak Hawkins-Simon condition.
The (weakly) sign symmetric -matrix completion problems.
The Wigner semi-circle law and the Heisenberg group
The Wigner Theorem states that the statistical distribution of the eigenvalues of a random Hermitian matrix converges to the semi-circular law as the dimension goes to infinity. It is possible to establish this result by using harmonic analysis on the Heisenberg group. In fact this convergence corresponds to the topology of the set of spherical functions associated to the action of the unitary group on the Heisenberg group.
Theorems of the alternative for cones and Lyapunov regularity of matrices
Standard facts about separating linear functionals will be used to determine how two cones and and their duals and may overlap. When is linear and and are cones, these results will be applied to and , giving a unified treatment of several theorems of the alternate which explain when contains an interior point of . The case when is the space of Hermitian matrices, is the positive semidefinite matrices, and yields new and known results about the existence of block diagonal...
Tilings associated with non-Pisot matrices
Suppose has a 2-dimensional expanding subspace , satisfies a regularity condition, called “good star”, and has , where is an oriented compound of . A morphism of the free group on is called a non-abelianization of if it has structure matrix . We show that there is a tiling substitution whose “boundary substitution” is a non-abelianization of . Such a tiling substitution leads to a self-affine tiling of with as its expansion. In the last section we find conditions on so...
Toeplitz band matrices with exponentially growing condition numbers.
Totally positive completions for monotonically labeled block clique graphs.
Trace inequalities with applications to orthogonal regression and matrix nearness problems.
Transformación de principios de consistencia aleatorios en determinísticos.
En la Teoría de la Decisión en Grupo, cuando los expertos emiten su información sobre los objetos de una manera probabilística, se pueden construir Principios de Consistencia que satisfagan los cinco principios de racionalidad y no sean dictatoriales [ver Sánchez-Pérez-Domench (1986)].Partiendo de esta situación, en el presente artículo se analizan y proponen diferentes métodos y algoritmos para transformar relaciones sociales aleatorias en determinísticas, continuando y completando así investigaciones...
Transformaciones que conservan el área.
Transformations preserving the Hankel transform.
Transforming stochastic matrices for stochastic comparison with the st-order
We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.
Transforming stochastic matrices for stochastic comparison with the st-order
We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.
Triangular stochastic matrices generated by infinitesimal elements
We show that each element in the semigroup of all non-singular upper (or lower) triangular stochastic matrices is generated by the infinitesimal elements of , which form a cone consisting of all upper (or lower) triangular intensity matrices.
Two applications of a bound on the Hadamard product with a Cauchy matrix.
Two characterizations of inverse-positive matrices: the Hawkins-Simon condition and the Le Chatelier-Braun principle.
Two contributions to the theory of coefficients of ergodicity