Abstract : The goal of the minisymposium is to stimulate research and foster interaction of researchers. It scope includes any topics in matrices and their applications. Matrix analysis is widely used in mathematics with applications in control and systems theory, image processing, operations research, scientific computing, statistics, and engineering. This minisymposium has multiple sessions which provide an opportunity for researchers to exchange ideas and recent developments in this active area of research. Participants are from Canada, China, Japan, Macau, Norway, Pakistan, Portugal, Singapore, South Korea, and USA.
Organizer(s) : Luyining Gan, Tin-Yau Tam, Qing-Wen Wang, Yang Zhang
[01267] Combinatorial Perron Parameters and Classes of Trees
Format : Talk at Waseda University
Author(s) :
Enide Cascais Andrade (CIDMA, University of Aveiro, Portugal)
Lorenzo Ciardo (University of Oxford)
Geir Dahl (University of Oslo)
Abstract :
The main goal of this talk is to present recent results related with the combinatorial Perron
parameters
introduced in previous papers for certain classes of trees, and related bounds for these parameters.
These parameters are related to algebraic connectivity of trees and corresponding centers.
[01379] Poset matrices and associated algebras
Format : Talk at Waseda University
Author(s) :
Gi-Sang Cheon (Sungkyunkwan University)
Abstract : We introduce the constructions of poset matrices by defining several partial compositions on the species of poset matrices. Some of these partial composition operations are shown to define a set operad structure. We also obtain various matrix algebras obtained from incidence algebras of Riordan posets.
[01266] Majorization orders for $(0,\pm 1)$-matrices
Format : Talk at Waseda University
Author(s) :
Geir Dahl (University of Oslo)
Alexander Guterman (Bar-Ilan University)
Pavel Shteyner (Bar-Ilan University)
Abstract : Matrix majorization is a generalization of classical majorization for vectors; an important notion in many areas of mathematics. The talk gives some majorization background, and then presents a study of matrix majorization for $(0, \pm 1)$-matrices, i.e., matrices whose entries are restricted to $0$, $1$ and $-1$. In particular, we characterize when the zero vector is weakly majorized by a matrix, and discuss related results. Different connections are discussed, and characterizations of majorization are given.
[00830] The ranks and decompositions of quaternion tensors
Format : Talk at Waseda University
Author(s) :
Yang Zhang (University of Manitoba)
Yungang Liang (University of Manitoba)
Abstract : Quaternion tensors have attracted more and more attentions in recent years. Many applications have been found in various areas. In this talk, we discuss the maximal ranks of quaternion tensors, in particular, the third-order case. We also investigate the canonical forms, CP and Tucker decompositions of some quaternion tensors.
[03621] Log-majorization and inequalities of power means
Format : Talk at Waseda University
Author(s) :
Sejong Kim (Chungbuk National University)
Abstract : As non-commutative versions of the quasi-arithmetic mean, we consider the Lim-Palfia’s power mean, Renyi right mean, and Renyi power mean of positive definite matrices. We see that the Lim-Palfia’s power mean of negative order converges increasingly to the log-Euclidean mean with respect to the weak log-majorization. Furthermore, we establish the weak log-majorization relationships between power means and provide the boundedness of Renyi power mean.
[00868] Matrix Problems in International Economics
Format : Talk at Waseda University
Author(s) :
Konstantin Kucheryavyy (University of Tokyo)
Abstract : Analyzing properties of general equilibrium models in economics amounts to analyzing properties of nonlinear systems of equations. The standard questions asked in this context are about existence and uniqueness of solutions to a nonlinear system of equations, characterization of multiplicity of solutions, and behavior of solutions in response to changes in parameters. One approach to address these questions is to formulate them in terms of matrix algebra. This approach has been especially fruitful when applied to classes of models arising in international economics. Such models often give rise to matrices with striking properties, but formally proving the observed properties usually constitutes a challenge. In my presentation, I will consider several matrix problems that arise in the international economics context and sketch related proofs. I will also discuss open questions in this literature.
[01404] Spectral inequalities for Kubo-Ando and Heinz means
Format : Talk at Waseda University
Author(s) :
Rute Correia Lemos (CIDMA, University of Aveiro)
Graça Soares (CMAT-UTAD, University of Trás-os Montes e Alto Douro)
Abstract : In this talk, spectral inequalities, involving Kubo-Ando operator connections and means of positive semidefinite matrices, are surveyed. Some Log-majorization type results are presented. Singular values inequalities for Heinz mean of matrices, which are not of Kubo-Ando type, and its 'harmonic' variant are also given.
[00800] Limit of the induced Aluthge transformations
Format : Talk at Waseda University
Author(s) :
Takeaki Yamazaki (Toyo University)
Abstract : Let $\mathcal{H}$ and $B(\mathcal{H})$ be a complex Hilbert space and the algebra of all bounded linear operators on $\mathcal{H}$, respectively. For $T\in B(\mathcal{H})$ with the polar decomposition $T=U|T|$, Aluthge transformation is known as $\Delta(T):=|T|^{1/2}U|T|^{1/2}$. In this talk, we shall introduce a generalization of Aluthge transformations and limit point of its iterations.
[01263] Geometric inequalities for contraction matrices
Format : Talk at Waseda University
Author(s) :
Tin-Yau Tam (University of Nevada, Reno)
Abstract : Given two $n\times n$ contraction matrices $W$ and $Z$, i.e., $I-WW^*\ge 0$ and $I-ZZ^*\ge 0$, L.K. Hua's inequalities (1955) assert that
$$
\det (I-WW^*)\det (I-ZZ^*) \le |\det (I - WZ^*)|^2\le \det (I+WW^*)\det (I+ZZ^*).
$$
In this talk we will present geometry behind Hua's inequalities in the context of elliptical and hyperbolic geometry.
[01307] The generalized quaternion matrix equation
Format : Talk at Waseda University
Author(s) :
Xin Liu (Macau University of Science and Technology)
Cui E Yu (Macau University of Science and Technology)
Abstract : We consider the matrix equation $AXB+CX^{\star}D=E$ over the generalized quaternions, where $X^\star$ is one of $X$, $X^\ast$, the $\eta$-conjugate or the $\eta$-conjugate transpose of $X$ with $\eta \in \{i, j, k\}$. We define two new real representations of a generalized quaternion matrix, then we derive the solvability conditions for the mentioned matrix equation. Moreover, we also discuss the existence of $X=\pm X^{\star}$ solutions to the generalized quaternion matrix equation $AXB+CXD=E$.
[01222] Some new results on matrix and tensor equations
Format : Online Talk on Zoom
Author(s) :
Qing-Wen Wang (Shanghai University, China)
Abstract : In this talk, we mainly introduce some new developments of matrix and tensor equations over the quaternion algebra.
[01920] Matrix inequalities and properties of means on positive definite matrices
Format : Online Talk on Zoom
Author(s) :
Luyining Gan (University of Nevada Reno)
Abstract : In this talk, we will introduce the study of the relations between the weighted metric geometric mean, the weighted spectral geometric mean and the weighted Wasserstein mean of the positive definite matrices in terms of (weak) log-majorization relation. In addition, we will also introduce some new properties of means, like geodesic property and tolerance relation.
[05621] How to chesk D-stability: a simple determinantal test
Format : Online Talk on Zoom
Author(s) :
Volha Y. Kushel (Shanghai University)
Abstract : The concept of matrix $D$-stability, introduced in 1958 by Arrow and McManus is of major importance due to the variety of its applications. However, characterization of matrix $D$-stability for dimensions $n > 4$ is considered as a hard open problem. In this talk, we propose a simple way for testing matrix $D$-stability, in terms of the inequalities between
principal minors of a matrix. The conditions are just sufficient but they allow to test matrices of an arbitrary size n, are easy to verify and can be used for the analysis of parameter-dependent models.
