The Electronic Journal of Linear Algebra <p>The Electronic Journal of Linear Algebra (ELA), a publication of the <a href="">International Linear Algebra Society (ILAS)</a>, is a refereed all-electronic journal that welcomes mathematical articles of high standards that contribute new information and new insights to matrix analysis and the various aspects of linear algebra and its applications.&nbsp;ELA is a JCR ranked journal, and indexed by MathSciNet, ZentralBlatt, and Scopus. &nbsp;ELA is completely free for authors/readers; and &nbsp;ELA is built on the selfless contributions of its authors, referees and editors.</p> <p><a href="" target="_blank" rel="noopener"><img src="" alt="" width="62" height="62"></a></p> International Linear Algebra Society en-US The Electronic Journal of Linear Algebra 1081-3810 A permanent inequality for positive semidefinite matrices <p>In this paper, we prove an inequality involving the permanent of a positive semidefinite matrix and its leading submatrices. We obtain a result in the similar spirit of Bapat-Sunder per-max conjecture.</p> Vehbi E. Paksoy Copyright (c) 2023 Vehbi E. Paksoy 2023-02-24 2023-02-24 39 71 77 10.13001/ela.2023.7701 Linear maps that preserve parts of the spectrum on pairs of similar matrices <p>In this paper, we characterize linear bijective maps $\varphi$ on the space of all $n \times n$ matrices over an algebraically closed field $\mathbb{F}$ having the property that the spectrum of $\varphi (A)$ and $\varphi (B)$ have at least one common eigenvalue for each similar matrices $A$ and $B$. Using this result, we characterize linear bijective maps having the property that the spectrum of $\varphi (A)$ and $\varphi (B)$ have common elements for each matrices $A$ and $B$ having the same spectrum. As a corollary, we also characterize linear bijective maps preserving the equality of the spectrum.</p> Constantin Costara Copyright (c) 2023 Constantin Costara 2023-03-23 2023-03-23 39 110 116 10.13001/ela.2023.7583 The inverse Horn problem <p>Alfred Horn's conjecture on eigenvalues of sums of Hermitian matrices was proved more than 20 years ago. In this note, the problem is raised of, given an $n$-tuple $\gamma$ in the solution polytope, constructing Hermitian matrices with the required spectra such that their sum has eigenvalues $\gamma$.</p> João Filipe Queiró Ana Paula Santana Copyright (c) 2023 João Filipe Queiró, Ana Paula Santana 2023-03-01 2023-03-01 39 90 93 10.13001/ela.2023.7539 Hypocoercivity and hypocontractivity concepts for linear dynamical systems <p>For linear dynamical systems (in continuous-time and discrete-time), we revisit and extend the concepts of hypocoercivity and hypocontractivity and give a detailed analysis of the relations of these concepts to (asymptotic) stability, as well as (semi-)dissipativity and (semi-)contractivity, respectively. On the basis of these results, the short-time behavior of the propagator norm for linear continuous-time and discrete-time systems is characterized by the (shifted) hypocoercivity index and the (scaled) hypocontractivity index, respectively.</p> Franz Achleitner Anton Arnold Volker Mehrmann Copyright (c) 2023 Franz Achleitner, Anton Arnold, Volker Mehrmann 2023-02-10 2023-02-10 39 33 61 10.13001/ela.2023.7531 An improved algorithm for solving an inverse eigenvalue problem for band matrices <p>The construction of matrices with prescribed eigenvalues is a kind of inverse eigenvalue problems. The authors proposed an algorithm for constructing band oscillatory matrices with prescribed eigenvalues based on the extended discrete hungry Toda equation (<em>Numer. Algor.</em> 75:1079--1101, 2017). In this paper, we develop a new algorithm for constructing band matrices with prescribed eigenvalues based on a generalization of the extended discrete hungry Toda equation. The new algorithm improves the previous algorithm so that the new one can produce more generic band matrices than the previous one in a certain sense. We compare the new algorithm with the previous one by numerical examples. Especially, we show an example of band oscillatory matrices which the new algorithm can produce but the previous one cannot.</p> Kanae Akaiwa Akira Yoshida Koichi Kondo Copyright (c) 2022 Kanae Akaiwa, Akira Yoshida, Koichi Kondo 2022-12-03 2022-12-03 39 745 759 10.13001/ela.2022.7475