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UW Digital - aggregated feedsenWySR RSS Feed: Brauer's theorem and nonnegative matrices with prescribed diagonal entries
https://repository.uwyo.edu/ela/vol35/iss1/5
<p>The problem of the existence and construction of nonnegative matrices with prescribed eigenvalues and diagonal entries is an important inverse problem, interesting by itself, but also necessary to apply a perturbation result, which has played an important role in the study of certain nonnegative inverse spectral problems.<p><a href="https://repository.uwyo.edu/ela/vol35/iss1/5">read more</a></p>
Fri, 15 Feb 2019 14:17:52 -0700WySR RSS Feed: Diagonal Sums of Doubly Substochastic Matrices
https://repository.uwyo.edu/ela/vol35/iss1/4
<p>Let $\Omega_n$ denote the convex polytope of all $n\times n$ doubly stochastic matrices, and $\omega_{n}$ denote the convex polytope of all $n\times n$ doubly substochastic matrices. For a matrix $A\in\omega_n$, define the sub-defect of $A$ to be the smallest integer $k$ such that there exists an $(n+k)\times(n+k)$ doubly stochastic matrix containing $A$ as a submatrix.<p><a href="https://repository.uwyo.edu/ela/vol35/iss1/4">read more</a></p>
Fri, 15 Feb 2019 14:17:33 -0700WySR RSS Feed: In-sphere property and reverse inequalities for matrix means
https://repository.uwyo.edu/ela/vol35/iss1/3
<p>The in-sphere property for matrix means is studied. It is proved that the matrix power mean satisfies in-sphere property with respect to the Hilbert-Schmidt norm. A new characterization of the matrix arithmetic mean is provided. Some reverse AGM inequalities involving unitarily invariant norms and operator monotone functions are also obtained.</p>Sat, 09 Feb 2019 18:41:40 -0700WySR RSS Feed: Surjective Additive Rank-1 Preservers on Hessenberg Matrices
https://repository.uwyo.edu/ela/vol35/iss1/2
<p>Let $H_{n}(\mathbb{F})$ be the space of all $n\times n$ upper Hessenberg matrices over a field~$\mathbb{F}$, where $n$ is a positive integer greater than two. In this paper, surjective additive maps preserving rank-$1$ on $H_{n}(\mathbb{F})$ are characterized.</p>Sat, 09 Feb 2019 18:41:29 -0700WySR RSS Feed: Solving the Sylvester Equation AX-XB=C when $\sigma(A)\cap\sigma(B)\neq\emptyset$
https://repository.uwyo.edu/ela/vol35/iss1/1
<p>The method for solving the Sylvester equation $AX-XB=C$ in complex matrix case, when $\sigma(A)\cap\sigma(B)\neq \emptyset$, by using Jordan normal form is given. Also, the approach via Schur decomposition is presented.</p>Tue, 05 Feb 2019 22:45:04 -0700WySR RSS Feed: Resolution Of Conjectures Related To Lights Out! And Cartesian Products
https://repository.uwyo.edu/ela/vol34/iss1/51
<p>Lights Out!\ is a game played on a $5 \times 5$ grid of lights, or more generally on a graph. Pressing lights on the grid allows the player to turn off neighboring lights. The goal of the game is to start with a given initial configuration of lit lights and reach a state where all lights are out.<p><a href="https://repository.uwyo.edu/ela/vol34/iss1/51">read more</a></p>
Wed, 16 Jan 2019 22:12:33 -0700WySR RSS Feed: On the Interval Generalized Coupled Matrix Equations
https://repository.uwyo.edu/ela/vol34/iss1/50
<p>In 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 ${\bf{A}}_{ij}$, ${\bf{B}}_{ik}$ and ${\bf{C}}_{i}$ are known real interval matrices, while $X_{j}$ and $Y_{k}$ are the unknown matrices for $j=1,\ldots,p$, $k=1,\ldots,q$<p><a href="https://repository.uwyo.edu/ela/vol34/iss1/50">read more</a></p>
Wed, 16 Jan 2019 22:12:23 -0700WySR RSS Feed: A note on linear preservers of semipositive and minimally semipositive matrices
https://repository.uwyo.edu/ela/vol34/iss1/49
<p>Semipositive matrices (matrices that map at least one nonnegative vector to a positive vector) and minimally semipositive matrices (semipositive matrices whose no column-deleted submatrix is semipositive) are well studied in matrix theory. In this short note, the structure of linear maps which preserve the set of all semipositive/minimally semipositive matrices is studied.<p><a href="https://repository.uwyo.edu/ela/vol34/iss1/49">read more</a></p>
Tue, 08 Jan 2019 12:59:04 -0700WySR RSS Feed: Vector Cross Product Differential and Difference Equations in R^3 and in R^7
https://repository.uwyo.edu/ela/vol34/iss1/48
<p>Through a matrix approach of the $2$-fold vector cross product in $\mathbb{R}^3$ and in $\mathbb{R}^7$, some vector cross product differential and difference equations are studied. Either the classical theory or convenient Drazin inverses, of elements belonging to the class of index $1$ matrices, are applied.</p>Tue, 08 Jan 2019 12:58:51 -0700WySR RSS Feed: Gershgorin type sets for eigenvalues of matrix polynomials
https://repository.uwyo.edu/ela/vol34/iss1/47
<p>New localization results for polynomial eigenvalue problems are obtained, by extending the notions of the Gershgorin set, the generalized Gershgorin set, the Brauer set and the Dashnic-Zusmanovich set to the case of matrix polynomials.</p>Wed, 26 Dec 2018 16:32:09 -0700