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Pure PSVD approach to Sylvester-type quaternion matrix equations
No full textIn this paper, the pure product singular value decomposition (PSVD) for four quaternion matrices is given. The system of coupled Sylvester-type quaternion matrix equations with five unknowns is considered by using the PSVD approach, where and are given quaternion matrices of compatible sizes . Some necessary and sufficient conditions for the existence of a solution to this system are derived. Moreover, the general solution to this system is presented when it is solvable
The inverse eigenvalue problem for Leslie matrices
No full textThe Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem of determining necessary and sufficient conditions for a list of complex numbers to be the spectrum of an entry--wise nonnegative matrix of dimension . This is a very difficult and long standing problem and has been solved only for . In this paper, the NIEP for a particular class of nonnegative matrices, namely Leslie matrices, is considered. Leslie matrices are nonnegative matrices, with a special zero--pattern, arising in the Leslie model, one of the best known and widely used models to describe the growth of populations. The lists of nonzero complex numbers that are subsets of the spectra of Leslie matrices are fully characterized. Moreover, the minimal dimension of a Leslie matrix having a given list of three numbers among its spectrum is provided. This result is partially extended to the case of lists of real numbers
Maps Preserving Norms of Generalized Weighted Quasi-arithmetic Means of Invertible Positive Operators
No full textIn this paper, the problem of describing the structure of transformations leaving norms of generalized weighted quasi-arithmetic means of invertible positive operators invariant is discussed. In a former result of the authors, this problem was solved for weighted quasi-arithmetic means, and here the corresponding result is generalized by establishing its solution under certain mild conditions. It is proved that in a quite general setting, generalized weighted quasi-arithmetic means on self-adjoint operators are not monotone in their variables which is an interesting property. Moreover, the relation of these means with the Kubo-Ando means is investigated and it is shown that the common members of the classes of these types of means are weighted arithmetic means
Wyoming, Take Another Look at Unions: How Unions Can Increase Equality for Women in the Workplace
No full textGeneralized Commuting Maps On The Set of Singular Matrices
No full textLet be the ring of all matrices over a field . In the present paper, additive mappings such that for all singular matrix will be characterized. Precisely, it will be proved that for all , where and is a central map. As an application, the description is given of all additive maps such that for all singular matrices , where
Surjective Additive Rank-1 Preservers on Hessenberg Matrices
No full textLet be the space of all upper Hessenberg matrices over a field~, where is a positive integer greater than two. In this paper, surjective additive maps preserving rank- on are characterized
On the Interval Generalized Coupled Matrix Equations
No full textIn this work, the interval generalized coupled matrix equations \begin{equation*} \sum_{j=1}^{p}{{\bf{A}}_{ij}X_{j}}+\sum_{k=1}^{q}{Y_{k}{\bf{B}}_{ik}}={\bf{C}}_{i}, \qquad i=1,\ldots,p+q, \end{equation*} are studied in which , and are known real interval matrices, while and are the unknown matrices for , and . This paper discusses the so-called AE-solution sets for this system. In these types of solution sets, the elements of the involved interval matrices are quantified and all occurrences of the universal quantifier (if any) precede the occurrences of the existential quantifier . The AE-solution sets are characterized and some sufficient conditions under which these types of solution sets are bounded are given. Also some approaches are proposed which include a numerical technique and an algebraic approach for enclosing some types of the AE-solution sets
Block GLT Sequences: Matrix Functions and Engineering Application
No full textThe theory of block generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the spectral distribution of block-structured matrices arising from the discretization of differential problems, with a special reference to systems of differential equations (DEs) and to the higher-order finite element or discontinuous Galerkin approximation of both scalar and vectorial DEs. In the present paper, the theory of block GLT sequences is extended by proving that is a block GLT sequence as long as is continuous and is a block GLT sequence formed by Hermitian matrices. It is also provided a relevant application of this result to the computation of the distribution of the numerical eigenvalues obtained from the higher-order isogeometric Galerkin discretization of second-order variable-coefficient differential eigenvalue problems (a topic of interest not only in numerical analysis but also in engineering)
Rightful Compensation for a Wrongful Conviction: In Defense of a Compensation Statute in the State of Wyoming
No full textConsistency of Quaternion Matrix Equations and
No full textFor a given ordered units triple , the solutions to the quaternion matrix equations and , , where is the conjugate transpose of , and , , are discussed. Some new real representations of quaternion matrices are used, which enable one to convert -conjugate (transpose) matrix equations into some real matrix equations. By using this idea, conditions for the existence and uniqueness of solutions to the above quaternion matrix equations are derived. Also, methods to construct the solutions from some related real matrix equations are presented