The Electronic Journal of Linear Algebra https://journals.uwyo.edu/index.php/ela <p>The Electronic Journal of Linear Algebra (ELA), a publication of the <a href="https://www.ilasic.org/">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="https://en.wikipedia.org/wiki/Electronic_Journal_of_Linear_Algebra" target="_blank" rel="noopener"><img src="https://journals.uwyo.edu/public/site/images/dopico/wikipedia.png" alt="" width="62" height="62"></a></p> International Linear Algebra Society en-US The Electronic Journal of Linear Algebra 1081-3810 The maximal angle between 5×5 positive semidefinite and 5×5 nonnegative matrices https://journals.uwyo.edu/index.php/ela/article/view/6647 <p>The paper is devoted to the study of the maximal angle between the $5\times 5$ semidefinite matrix cone and $5\times 5$ nonnegative matrix cone. A signomial geometric programming problem is formulated in the process to find the maximal angle. Instead of using an optimization problem solver to solve the problem numerically, the method of Lagrange Multipliers is used to solve the signomial geometric program, and therefore, to find the maximal angle between these two cones.</p> Qinghong Zhang Copyright (c) 2021 Qinghong Zhang 2021-11-19 2021-11-19 37 698 708 10.13001/ela.2021.6647 (0,1)-matrices and discrepancy https://journals.uwyo.edu/index.php/ela/article/view/5033 <p>&nbsp;Let $m$ and $n$ be positive integers, and let $R =(r_1, \ldots, r_m)$ and $S =(s_1,\ldots, s_n)$ be nonnegative integral vectors. Let $A(R,S)$ be the set of all $m \times n$ $(0,1)$-matrices with row sum vector $R$ and column vector $S$. Let $R$ and $S$ be nonincreasing, and let $F(R)$ be the $m \times n$ $(0,1)$-matrix where for each $i$, the $i^{th}$ row of $F(R,S)$ consists of $r_i$ 1's followed by $n-r_i$ 0's. Let $A\in A(R,S)$. The discrepancy of A, $disc(A)$, is the number of positions in which $F(R)$ has a 1 and $A$ has a 0. In this paper, we investigate the possible discrepancy of $A^t$ versus the discrepancy of $A$. We show that if the discrepancy of $A$ is $\ell$, then the discrepancy of the transpose of $A$ is at least $\frac{\ell}{2}$ and at most $2\ell$. These bounds are tight.</p> LeRoy Beasley Copyright (c) 2021-11-18 2021-11-18 37 692 697 10.13001/ela.2021.5033 Centrosymmetric universal realizability https://journals.uwyo.edu/index.php/ela/article/view/5781 <p>A list $\Lambda =\{\lambda_{1},\ldots,\lambda_{n}\}$ of complex numbers is said to be <em>realizable</em>, if it is the spectrum of an entrywise nonnegative matrix $A$. In this case, $A$ is said to be a <em>realizing matrix</em>. $\Lambda$ is said to be <em>universally realizable</em>, if it is realizable for each possible Jordan canonical form (JCF) allowed by $\Lambda$. The problem of the universal realizability of spectra is called the <em>universal realizability problem</em> (URP). Here, we study the centrosymmetric URP, that is, the problem of finding a nonnegative centrosymmetric matrix for each JCF allowed by a given list $\Lambda$. In particular, sufficient conditions for the centrosymmetric URP to have a solution are generated.</p> Ana Julio Yankis R. Linares Ricardo L. Soto Copyright (c) 2021-11-03 2021-11-03 37 680 691 10.13001/ela.2021.5781 Polar decompositions of quaternion matrices in indefinite inner product spaces https://journals.uwyo.edu/index.php/ela/article/view/6411 <p>Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an $H$-polar decomposition are found. In the process, an equivalent to Witt's theorem on extending $H$-isometries to $H$-unitary matrices is given for quaternion matrices.</p> Gilbert J. Groenewald Dawie B. Janse van Rensburg André C.M. Ran Frieda Theron Madelein van Straaten Copyright (c) 2021-10-29 2021-10-29 37 659 670 10.13001/ela.2021.6411 Simple necessary conditions for Hadamard factorizability of Hurwitz polynomials https://journals.uwyo.edu/index.php/ela/article/view/5957 <p>In this paper, we focus the attention on the Hadamard factorization problem for Hurwitz polynomials. We give a new necessary condition for Hadamard factorizability of Hurwitz stable polynomials of degree $n\geq 4$ and show that for $n= 4$ this condition is also sufficient. The effectiveness of the result is illustrated during construction of examples of stable polynomials that are not Hadamard factorizable.</p> Stanisław Białas Michał Góra Copyright (c) 2021-10-27 2021-10-27 37 671 679 10.13001/ela.2021.5957