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. ELA is a JCR ranked journal, and indexed by MathSciNet, ZentralBlatt, and Scopus. ELA is completely free for authors/readers; and 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 Societyen-USThe Electronic Journal of Linear Algebra1081-3810Trees with maximum sum of the two largest Laplacian eigenvalues
https://journals.uwyo.edu/index.php/ela/article/view/7065
<p>Let $T$ be a tree of order $n$ and $S_2(T)$ be the sum of the two largest Laplacian eigenvalues of $T$. Fritscher <em>et al.</em> proved that for any tree $T$ of order $n$, $S_2(T) \leq n+2-\frac{2}{n}$. Guan <em>et al.</em> determined the tree with maximum $S_2(T)$ among all trees of order $n$. In this paper, we characterize the trees with $S_2(T) \geq n+1$ among all trees of order $n$ except some trees. Moreover, among all trees of order $n$, we also determine the first $\lfloor\frac{n-2}{2}\rfloor$ trees according to their $S_2(T)$. This extends the result of Guan <em>et al.</em></p>Yirong ZhengJianxi LiSarula Chang
Copyright (c) 2022 Yirong Zheng, Jianxi Li, Sarula Chang
2022-07-152022-07-1535736610.13001/ela.2022.7065Positive linear maps and spreads of normal matrices
https://journals.uwyo.edu/index.php/ela/article/view/7009
<p>We obtain some inequalities involving positive linear maps on matrix algebra. The special cases provide bounds for the spreads of normal matrices.</p>Rajesh SharmaManish Pal
Copyright (c) 2022 Rajesh Sharma, Manish Pal
2022-06-212022-06-2134735610.13001/ela.2022.7009K-subdirect sums of Nekrasov matrices
https://journals.uwyo.edu/index.php/ela/article/view/6951
<p>In this paper, we give a sufficient and necessary condition for the subdirect sum of a Nekrasov matrix and a strictly diagonally dominant matrix being still a Nekrasov matrix. Adopting this sufficient and necessary condition, we present several simple sufficient conditions ensuring that the subdirect sum of Nekrasov matrices is in the same class. Examples are reported to illustrate the theoretical results.</p>Zhen-Hua LyuXueru WangLishu Wen
Copyright (c) 2022 Zhen-Hua Lyu, Xueru Wang, Lishu Wen
2022-06-102022-06-1033934610.13001/ela.2022.6951Linear maps preserving the Lorentz spectrum: the $2 \times 2$ case
https://journals.uwyo.edu/index.php/ela/article/view/6925
<p>In this paper, a complete description of the linear maps $\phi:W_{n}\rightarrow W_{n}$ that preserve the Lorentz spectrum is given when $n=2$, and $W_{n}$ is the space $M_{n}$ of $n\times n$ real matrices or the subspace $S_{n}$ of $M_{n}$ formed by the symmetric matrices. In both cases, it has been shown that $\phi(A)=PAP^{-1}$ for all $A\in W_{2}$, where $P$ is a matrix with a certain structure. It was also shown that such preservers do not change the nature of the Lorentz eigenvalues (that is, the fact that they are associated with Lorentz eigenvectors in the interior or on the boundary of the Lorentz cone). These results extend to $n=2$ those for $n\geq 3$ obtained by Bueno, Furtado, and Sivakumar (2021). The case $n=2$ has some specificities, when compared to the case $n\geq3,$ due to the fact that the Lorentz cone in $\mathbb{R}^{2}$ is polyedral, contrary to what happens when it is contained in $\mathbb{R}^{n}$ with $n\geq3.$ Thus, the study of the Lorentz spectrum preservers on $W_n = M_n$ also follows from the known description of the Pareto spectrum preservers on $M_n$.</p>MarĂa I. BuenoSusana FurtadoAelita KlausmeierJoey Veltri
Copyright (c) 2022 M. I. Bueno, Susana Furtado, Aelita Klausmeier, Joey Veltri
2022-06-022022-06-0231733010.13001/ela.2022.6925Majorization inequalities via convex functions
https://journals.uwyo.edu/index.php/ela/article/view/6901
<p>Convex functions have been well studied in the literature for scalars and matrices. However, other types of convex functions have not received the same attention given to the usual convex functions. The main goal of this article is to present matrix inequalities for many types of convex functions, including log-convex, harmonically convex, geometrically convex, and others. The results extend many known results in the literature in this direction. <br>For example, it is shown that if $A,B$ are positive definite matrices and $f$ is a continuous $\sigma\tau$-convex function on an interval containing the spectra of $A,B$, then<br>\begin{align*}<br>\lambda^\downarrow (f(A\sigma B))\prec_w\lambda^\downarrow \left(f(A)\tau f(B)\right),<br>\end{align*}<br>for the matrix means $\sigma,\tau\in\{\nabla_{\alpha},!_{\alpha}\}$ and $\alpha\in[0,1]$. Further, if $\sigma=\sharp_{\alpha}$, then<br>\begin{align*} \lambda^\downarrow \left(f\left(e^{A\nabla_{\alpha}B}\right)\right)\prec_w\lambda^\downarrow \left(f(e^A)\tau f(e^B))\right).<br>\end{align*}<br>Similar inequalities will be presented for two-variable functions too.</p>Mohsen KianMohammad Sababheh
Copyright (c) 2022 Mohsen Kian, Mohammad Sababheh
2022-02-222022-02-2217919410.13001/ela.2022.6901