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Steven Miller (Williams College)5/18/26, 11:00 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
Random matrix theory has successfully modeled a variety of systems, from energy levels of heavy nuclei to zeros of the Riemann zeta function. One of the central results is Wigner's semi-circle law: the distribution of normalized eigenvalues for ensembles of real symmetric matrices converge to the semi-circle density (in some sense) as the matrix size tends to infinity. We introduce a new...
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Motoyuki NOBORI (Graduate School of Science and Engineering, Ehime University)5/18/26, 11:25 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
The main purpose of this presentation is to illustrate an equivalent condition for the equality case in the generalized Böttcher-Wenzel (BW) inequality for three matrices.
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Let $A, B,$ and $C$ be square matrices with complex elements. The BW inequality is an upper bound estimate on the Frobenius norm of the commutator of $A$ and $B$, defined as $AB-BA$. After the BW inequality was proved in... -
Fuzhen Zhang (Nova Southeastern University)5/18/26, 11:50 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
Normal matrices form a central class in matrix analysis, including Hermitian, skew-Hermitian, and unitary, positive semidefinite, permutation matrices and so on. This presentation surveys fundamental properties of normal matrices, including spectral characterization, unitary diagonalization, and trace (in)equality through majorization. It highlights equivalent conditions for normality, with...
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John Peca-Medlin (UCSD)5/18/26, 2:00 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
Gaussian elimination with partial pivoting (GEPP) remains the most widely used dense linear solver. GEPP produces the factorization $PA = LU$, where $L$ and $U$ are lower and upper triangular matrices and $P$ is a permutation matrix; together, these encode the pivoting strategy, directly influencing stability through classical growth-factor bounds and matrix norm inequalities. When $A$ is...
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Mohsen Aliabadi (Clayton State University)5/18/26, 2:25 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
We survey classical results in additive combinatorics and develop linear analogues over field extensions, with an emphasis on Kneser-type phenomena. In addition to recalling Kneser's theorem and stabilizer methods (including Cauchy--Davenport and DeVos's refinement), we present a rigidity theorem showing that if $|A+B|=|A|+|B|-1$ with $A+B\neq G$, then $A+B$ is a subgroup and $A$ is a coset;...
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Marko Orel (University of Primorska)5/18/26, 2:50 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
The matrix equation $rank(A-B)=1$ is well studied in linear algebra and combinatorics within preserver problems and the theory of distance-regular graphs/association schemes. In the talk I will present how this equality is related to coding theory, namely to binary self-dual codes.
Let $\widehat{\Gamma}_{n}$ be the graph with the vertex set formed by all $n\times n$ symmetric...
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Tanvi Jain (Indian Statistical Institute)5/19/26, 11:00 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
We discuss majorisation inequalities for different means of positive definite matrices focusing on the geometric mean, the Wasserstein mean, the log Euclidean mean and the power mean.
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Dr Xuzhou Zhan (Beijing Normal University at Zhuhai)5/19/26, 11:25 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
This talk focuses on several stability criteria via Markov parameters for regular matrix polynomials, which generalize the corresponding criteria constrained by the monic assumption. The testing framework employs two finite Hankel matrices, whose rectangular blocks are the submatrices of the Markov parameters redefined through a column-wise splitting and column reduction for matrix...
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Dominique Guillot (University of Delaware)5/19/26, 11:50 AMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
We consider general bilinear products parameterized by positive semidefinite matrices. Typically non-commutative, non-associative, and non-unital, these products preserve positivity and include the classical Hadamard, Kronecker, and convolutional products as special cases. We prove that every such product satisfies a sharp nonzero lower bound in the Loewner order, generalizing previous results...
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Prateek Kumar Vishwakarma (Universite Laval, Quebec, Canada)5/19/26, 2:00 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
Classical approaches to matrix function theory — i.e., extending scalar functions to matrices — are largely organized around two frameworks: entrywise calculus via the Schur (Hadamard) product, and functional calculus via the spectral theorem. In this talk, I present a third, fundamentally different framework based on matrix convolution, in which convolution itself is viewed as a matrix...
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Jie Tian (University of Nevada, Reno)5/19/26, 2:25 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
The quaternionic numerical range of a matrix is generally nonconvex, in contrast to the classical complex case. Nevertheless, a theorem of So and Thompson in 1996 asserts that the associated \emph{upper bild} in the complex upper half-plane is always convex.
The original proof of So and Thompson relies on a detailed case-by case and computationally involved analysis, including a reduction...
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Meiling Deng (University of Nevada, Reno)5/19/26, 2:50 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
In this talk, we investigate the eigenvalue problem for third-order quaternionic tensors. We first introduce the notion of right T-eigenvalues and develop an efficient algorithm for their computation, whose effectiveness is demonstrated through comparative numerical experiments.
For Hermitian quaternionic tensors, we then derive bounds for the eigenvalues of tensor sums and extend Weyl’s...
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Ms Mamta Verma (Dr B R Ambedkar National Institute of Technology Jalandhar, 144008, Punjab, India)5/19/26, 3:45 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
In this work, we study some inequalities for positive linear maps in the context of spectral graph theory. In particular, we present both existing and new bounds for the spread of matrices associated with graphs, expressed in terms of graph invariants.
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Fengjiao Liu (FAMU-FSU College of Engineering)5/19/26, 4:10 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
In this talk, we first investigate the maximal interval of existence for the solution of a symmetric matrix Riccati differential equation. Then, we apply this result to study the reachability of the closed-loop state transition matrix for a linear time-varying system over a finite time interval. Under a mild assumption, we characterize the set of closed-loop terminal state transition matrices...
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Joshua Cooper (University of South Carolina)5/19/26, 4:35 PMMatrix Inequalities, Matrix Equations, and Their ApplicationsMinisymposium Talk
Pressing sequences of simple undirected graphs totally colored by a field arise naturally in computational phylogenetics, where (over $GF(2)$) they are in bijection with sortings-by-reversal of signed permutations which model gene sequences in related organisms. They can be viewed in several surprising different ways, including as any consecutive initial sequence of rows whose diagonal...
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