BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shaun Fallat (University of Regina) DTSTART:20210209T000000Z DTEND:20210209T005000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/1 DESCRIPTION:Title: Implications of “Strong” Matrix Properties to an Inver se Eigenvalue Problem of Graphs\nby Shaun Fallat (University of Regina ) as part of 2021 UNR Spring Matrix Seminar\n\n\nAbstract\nThe inverse eig envalue problem for G (IEP-G) asks to determine if a given multi-set of re al numbers is the spectrum of a matrix in S(G). This particular variant on the IEP-G was born from the research of Parter and Wiener concerning the eigenvalue of trees and evolved more recently with a concentration on rela ted parameters such as: minimum rank\, maximum multiplicity\, minimum numb er of distinct eigenvalues\, and zero forcing numbers. An exciting aspect of this problem is the interplay with other areas of mathematics and appli cations. A novel avenue of research on so-called `strong properties' of ma trices\, closely tied to the implicit function theorem\, provides algebrai c conditions on a matrix with a certain spectral property and graph that g uarantee the existence of a matrix with the same spectral property for a f amily of related graphs.\n\nIn this lecture\, we will review some of the h istory and motivation of the IEP-G. Building on the work Colin de Verdi\\' ere\, we will discuss some of these newly developed `strong properties' an d present a number of interesting applications pertaining to the IEP-G.\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jephian Chin-Hung Lin (National Sun Yat-sen University) DTSTART:20210223T000000Z DTEND:20210223T005000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/2 DESCRIPTION:Title: Zero Forcing and its Applications\nby Jephian Chin-Hun g Lin (National Sun Yat-sen University) as part of 2021 UNR Spring Matrix Seminar\n\n\nAbstract\nIn a linear equation\, if all variables are known e xcept for one\, then this variable is also known. Based on this simple fac t\, zero forcing is a color-changing game that mimics the growing of known information. It was first developed independently for nullity control in mathematics and quantum control in physics. Many applications were then fo und afterwards. We will discuss how to use zero forcing to determine the s ensor deployment of an electronic network\, and we will introduce a techni que of using zero forcing to guarantee the strong spectral property.\nA sy mmetric matrix $A$ is said to have the strong spectral property if $X=O$ i s the only symmetric matrix that satisfies $A\\circ X=O\, I\\circ X=O\, an d AX-XA=O$. Here the operation is the entrywise product. If a matrix\nhas the strong spectral property\, then one may perturb the matrix slightly t o create more nonzero entries without changing its spectrum. This behavior has been used widely for constructing matrices in the inverse eigenvalue problem of a graph. In this talk\, we will show that if the nonzero patter n of the matrix is described by certain graphs\, then it always has the st rong spectral property.\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Plosker (Brandon University) DTSTART:20210302T000000Z DTEND:20210302T005000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/3 DESCRIPTION:Title: Centrosymmetric Stochastic Matrices\nby Sarah Plosker (Brandon University) as part of 2021 UNR Spring Matrix Seminar\n\n\nAbstra ct\nWe consider the convex subset of m by n stochastic matrices that are c entrosymmetric: stochastic matrices that are symmetric under rotation by 1 80 degrees. We consider the extreme points and bases of this set\, as well as several other parameters associated to such matrices. We provide examp les illustrating the results throughout. This is joint work with Lei Cao ( Nova Southeastern University) and Darian McLaren (University of Waterloo)\ n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonard Huang (University of Nevada Reno) DTSTART:20210309T000000Z DTEND:20210309T005000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/4 DESCRIPTION:Title: An Elementary Proof of a Decomposition Result for Poincar é Transformations\nby Leonard Huang (University of Nevada Reno) as pa rt of 2021 UNR Spring Matrix Seminar\n\n\nAbstract\nThe Poincaré transfor mations are the most general coordinate transformations between inertial r eference frames in Minkowski spacetime that preserve spacetime intervals. It is well known that every Poincaré transformation can be expressed as a composition of a Lorentz boost\, a spatial rotation\, a spatial reflectio n\, and a temporal reflection. Most proofs of this decomposition result re ly on concepts from Lie groups and Lie algebras\, which make them difficul t for undergraduate students to understand. In this talk\, we shall offer an alternative proof that uses only basic techniques from linear algebra ( such as those taught in MATH 330)\, with the most advanced concept utilize d being that of polar decomposition. This is joint work with Ava Covington \, a freshman at UNR majoring in Physics.\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Pan-Shun Lau (University of Nevada Reno) DTSTART:20210315T230000Z DTEND:20210315T235000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/5 DESCRIPTION:Title: The C-numerical Range of Matrices\nby Pan-Shun Lau (Un iversity of Nevada Reno) as part of 2021 UNR Spring Matrix Seminar\n\nAbst ract: TBA\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Huajun Huang (Auburn University) DTSTART:20210322T230000Z DTEND:20210322T235000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/6 DESCRIPTION:Title: Trace Preserving Properties and Invertible Completely Posi tive Maps\nby Huajun Huang (Auburn University) as part of 2021 UNR Spr ing Matrix Seminar\n\n\nAbstract\nWe describe maps $\\phi_1\,\\ldots\,\\ph i_m$ between various matrix spaces that satisfy the trace preserving prope rties $Tr(\\phi_1(A_1)\\cdots\\phi_m(A_m))=Tr(A_1\\cdots A_m)$\, and explo re the connection of this problem to invertible completely positive maps i n quantum information theory\, which could be used in quantum decoding and quantum error correction.\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis Verde (Metropolitan Autonomous University) DTSTART:20210329T230000Z DTEND:20210329T235000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/7 DESCRIPTION:Title: Matrices of coefficients of hypergeometric orthogonal poly nomial sequences and their connections with linearly recurrent sequences\nby Luis Verde (Metropolitan Autonomous University) as part of 2021 UNR Spring Matrix Seminar\n\n\nAbstract\nLet $v_k(t)$ and $u_k(t)$ be monic polynomials of degree $k$\, for $k \\ge 0$.\nThen \n$$u_n(t) = \\sum_{k=0 }^n c_{n\,k} v_k(t)\, \\qquad n \\ge 0.$$\nThe matrix $C=[c_{n\,k}]$ is a n infinite lower triangular invertible matrix.\nAn important problem in th e theory of orthogonal polynomial sequences is the following:\n\nFind $v_k (t)$ and $C$ such that the polynomials $u_k(t)$ satisfy a three-term recur rence relation of the form \n$$ u_{n+1}(t)=(t-\\beta_n) u_n(t) - \\alpha_n u_{n-1}(t)\, \\qquad n \\ge 1\, $$\nand the $u_k$ are eigenvectors of cer tain generalized difference operators.\n\nWe will show how this problem is solved using some linearly recurrent sequences of order 3 and taking the basis $\\{v_k(t): k \\ge 0\\}$ as the Newton basis associated with a seq uence of nodes that is linearly recurrent.\nThe main step is proving that certain matrix that is constructed using $C$\, $C^{-1}$\, and a pair of sequences\, is tridiagonal.\n\nOur construction produces all the hyperge ometric and basic hypergeometric orthogonal polynomial families.\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kijti Rodtes (Naresuan University) DTSTART:20210405T230000Z DTEND:20210405T235000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/8 DESCRIPTION:Title: Multinomial Vandermonde Convolution via Permanent\nby Kijti Rodtes (Naresuan University) as part of 2021 UNR Spring Matrix Semin ar\n\n\nAbstract\nIn this talk\, a generalized Laplace expansion for the p ermanent function will be provided. As a consequence\, a multinomial Vand ermonde convolution can be reproved. Also\, some combinatorial identities are also discussed by applying special matrices to the expansion.\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Mehmet Gumus (University of Nevada Reno) DTSTART:20210412T230000Z DTEND:20210412T235000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/9 DESCRIPTION:Title: Some New Results on Positive Semi-Denite Block Matrices\nby Mehmet Gumus (University of Nevada Reno) as part of 2021 UNR Spring Matrix Seminar\n\n\nAbstract\nIn this talk\, we will present several recen t developments on positive semi-definite block matrices. We will consider the norm inequalities\, the trace inequalities\, and a characterization fo r some special types of positive partial transpose matrices. Several open problems will also be discussed.\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Kuo-Zhong Wang (National Chiao Tung University) DTSTART:20210419T230000Z DTEND:20210419T235000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/10 DESCRIPTION:Title: Numerical ranges of matrix powers\nby Kuo-Zhong Wang (National Chiao Tung University) as part of 2021 UNR Spring Matrix Seminar \n\n\nAbstract\nFor any $n$-by-$n$ complex matrix $A$\, its numerical rang e $W(A)$ is defined by $\\{x^*Ax:x\\in \\mathbb{C}^n\,x^*x=1\\}$. The stud y of the numerical range has a history of one hundred years now. It starte d with the amazing result of Toeplitz-Hausdorff that the numerical range i s always a convex set in the plane. $W(A)$ is a set that can be used to le arn something about the matrix $A$\, and it can often give information tha t the spectrum alone cannot give. In this talk\, we start to present some basic properties of the numerical range of a matrix. Then we will introduc e some recent results and problems on this topic.\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Yongdo Lim (Sungkyunkwan University) DTSTART:20210426T230000Z DTEND:20210426T235000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/11 DESCRIPTION:Title: The Karcher mean of $2\\times 2$ triples\nby Yongdo L im (Sungkyunkwan University) as part of 2021 UNR Spring Matrix Seminar\n\n \nAbstract\nA long-standing open problem for the Karcher (alternatively\, Riemannian or Cartan) mean \nof positive definite matrices is to find its closed-form expression\, \nwhich is still unsolved even for $2 \\times 2$ triples. In this talk\, we present a recent development \nof the Karcher m ean for $2 \\times 2$ triples.\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Frank Hall (Georgia State University) DTSTART:20210503T230000Z DTEND:20210503T235000Z DTSTAMP:20260404T110742Z UID:UNRMatrixSeminar/12 DESCRIPTION:Title: G-matrices\, J-orthogonal matrices\, and their sign patte rns\nby Frank Hall (Georgia State University) as part of 2021 UNR Spri ng Matrix Seminar\n\n\nAbstract\nA real matrix $A$ is a G-matrix if $A$ is nonsingular and there exist nonsingular diagonal matrices $D_1$ and $D_2$ such that\n$A^{-T}= D_1 AD_2$\, where $A^{-T}$ denotes the transpose of t he inverse of $A$.\nDenote by $J = {\\rm diag}(\\pm 1)$ a diagonal (signat ure) matrix\, each of whose diagonal entries is $+1$ or $-1$. A nonsingula r real matrix $Q$ is\ncalled J-orthogonal if $Q^TJ Q=J$.\n\nThe G-matrices form a rich class of matrices that include the J-orthogonal matrices. In this talk\, many connections are made between these two types of matrices. \nIn particular\, a matrix $A$ is a G-matrix if and only if $A$ is diagon ally (with positive diagonals) equivalent to a column (or row) permutation of a \nJ-orthogonal matrix. An investigation into the sign patterns of th ese matrices is explored. It is observed that the sign patterns of the G-m atrices are \nexactly the permutation equivalences of the sign patterns of the J-orthogonal matrices.\n\nSign potentially J-orthogonal conditions ar e also considered. Some open questions are presented and continuing work i s discussed. \nThis research is joint with several authors including Miros lav Fiedler and Miro Rozloznik of the Czech Academy of Sciences.\n LOCATION:https://stable.researchseminars.org/talk/UNRMatrixSeminar/12/ END:VEVENT END:VCALENDAR