Rukhin, Andrew L.

In the random-effects model of meta-analysis a canonical representation of the restricted likelihood function is obtained. This representation relates the mean effect and the heterogeneity variance estimation problems. An explicit form of the variance of weighted means statistics determined by means of a quadratic form is found. The behavior of the...

Shao, Meiyue

Computing the exponential of large-scale skew-Hermitian matrices or parts thereof is frequently required in applications. In this work, we consider the task of extracting finite diagonal blocks from a doubly-infinite skew-Hermitian matrix. These matrices usually have unbounded entries which impede the application of many classical techniques from a...

Pereira, Rajesh Plosker, Sarah

We consider recent work linking majorization and trumping, two partial orders that have proven useful with respect to the entanglement transformation problem in quantum information, with general Dirichlet polynomials, Mellin transforms, and completely monotone sequences. We extend a basic majorization result to the more physically realistic infinit...

Futorny, Vyacheslav Rybalkina, Tetiana Sergeichuk, Vladimir V.

We give a method for constructing a regularizing decomposition of a matrix pencil, which is formulated in terms of the linear mappings. We prove that two pencils are topologically equivalent if and only if their regularizing decompositions coincide up to permutation of summands and their regular parts coincide up to homeomorphisms of their spaces.

Cirici, Joana

We study the varieties of invariant totally geodesic submanifolds of isometries of the spherical, Euclidean and hyperbolic spaces in each finite dimension. We show that the dimensions of the connected components of these varieties determine the orbit type (or the z-class) of the isometry. For this purpose, we introduce the Segre symbol of an isomet...

De Marchi, Stefano Usevich, Konstantin

We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma 1, L. Bos et al. (2009), Dolomites Research Notes on Approximation, 2:1-15]. As a special case, we apply the r...

Agore, A. L.

For a given extension $A \subset E$ of associative algebras we describe and classify up to an isomorphism all $A$-complements of $E$, i.e. all subalgebras $X$ of $E$ such that $E = A + X$ and $A \cap X = \{0\}$. Let $X$ be a given complement and $(A, \, X, \, \triangleright, \triangleleft, \leftharpoonup, \rightharpoonup \bigl)$ the canonical match...

Aguirre Holguín, Valeria Wojciechowski, Piotr J.
Published in
Linear Algebra and Its Applications

A special class of matrix algebras, the rc-signature algebras, naturally emerged as a result of the study of a Multiplicative Decomposition Property of matrices (a multiplicative analogue of the Riesz Decomposition Property in ordered vector spaces). This note is devoted to the study of a tractable subclass of these algebras. It is proven that a ne...

Peña, J.M.
Published in
Linear Algebra and Its Applications

A matrix is almost strictly totally positive if all its minors are nonnegative and they are positive if and only if they do not contain a zero in their diagonal. An optimal test to check if a given matrix belongs to this class of matrices is presented. For this purpose, we establish a bijection between the set of nonzero entries of the matrix and a...

Melman, A.
Published in
Linear Algebra and Its Applications

We generalize several Cauchy-like inclusion regions for the zeros of a polynomial expressed in a basis defined by a three-term recurrence relation. Our results are obtained by applying linear algebra techniques to the comrade matrix of a polynomial. We pay special attention to the Newton and Chebyshev bases.