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:20260422T225658Z UID:UNRMatrixSeminar/1 DESCRIPTION:Title: Implications of “Strong” Matrix Properties to an Inverse Eige nvalue Problem of Graphs\nby Shaun Fallat (University of Regina) as pa rt of 2021 UNR Spring Matrix Seminar\n\n\nAbstract\nThe inverse eigenvalue problem for G (IEP-G) asks to determine if a given multi-set of real numb ers is the spectrum of a matrix in S(G). This particular variant on the IE P-G was born from the research of Parter and Wiener concerning the eigenva lue of trees and evolved more recently with a concentration on related par ameters such as: minimum rank\, maximum multiplicity\, minimum number of d istinct eigenvalues\, and zero forcing numbers. An exciting aspect of this problem is the interplay with other areas of mathematics and applications . A novel avenue of research on so-called `strong properties' of matrices\ , closely tied to the implicit function theorem\, provides algebraic condi tions on a matrix with a certain spectral property and graph that guarante e the existence of a matrix with the same spectral property for a family o f related graphs.\n\nIn this lecture\, we will review some of the history and motivation of the IEP-G. Building on the work Colin de Verdi\\'ere\, w e will discuss some of these newly developed `strong properties' and prese nt a number of interesting applications pertaining to the IEP-G.\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jephian Chin-Hung Lin (National Sun Yat-sen University) DTSTART:20210223T000000Z DTEND:20210223T005000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/2 DESCRIPTION:Title: Zero Forcing and its Applications\nby Jephian Chin-Hung 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 except f or one\, then this variable is also known. Based on this simple fact\, zer o forcing is a color-changing game that mimics the growing of known inform ation. It was first developed independently for nullity control in mathema tics and quantum control in physics. Many applications were then found aft erwards. We will discuss how to use zero forcing to determine the sensor d eployment of an electronic network\, and we will introduce a technique of using zero forcing to guarantee the strong spectral property.\nA symmetric matrix $A$ is said to have the strong spectral property if $X=O$ is the o nly symmetric matrix that satisfies $A\\circ X=O\, I\\circ X=O\, and AX-XA =O$. Here the operation is the entrywise product. If a matrix\nhas the st rong spectral property\, then one may perturb the matrix slightly to creat e more nonzero entries without changing its spectrum. This behavior has be en used widely for constructing matrices in the inverse eigenvalue problem of a graph. In this talk\, we will show that if the nonzero pattern of th e matrix is described by certain graphs\, then it always has the strong sp ectral property.\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Plosker (Brandon University) DTSTART:20210302T000000Z DTEND:20210302T005000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/3 DESCRIPTION:Title: Centrosymmetric Stochastic Matrices\nby Sarah Plosker (Brando n University) as part of 2021 UNR Spring Matrix Seminar\n\n\nAbstract\nWe consider the convex subset of m by n stochastic matrices that are centrosy mmetric: stochastic matrices that are symmetric under rotation by 180 degr ees. We consider the extreme points and bases of this set\, as well as sev eral other parameters associated to such matrices. We provide examples ill ustrating the results throughout. This is joint work with Lei Cao (Nova So utheastern University) and Darian McLaren (University of Waterloo)\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonard Huang (University of Nevada Reno) DTSTART:20210309T000000Z DTEND:20210309T005000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/4 DESCRIPTION:Title: An Elementary Proof of a Decomposition Result for Poincaré Trans formations\nby Leonard Huang (University of Nevada Reno) as part of 20 21 UNR Spring Matrix Seminar\n\n\nAbstract\nThe Poincaré transformations are the most general coordinate transformations between inertial reference frames in Minkowski spacetime that preserve spacetime intervals. It is we ll known that every Poincaré transformation can be expressed as a composi tion of a Lorentz boost\, a spatial rotation\, a spatial reflection\, and a temporal reflection. Most proofs of this decomposition result rely on co ncepts from Lie groups and Lie algebras\, which make them difficult for un dergraduate students to understand. In this talk\, we shall offer an alter native proof that uses only basic techniques from linear algebra (such as those taught in MATH 330)\, with the most advanced concept utilized being that of polar decomposition. This is joint work with Ava Covington\, a fre shman at UNR majoring in Physics.\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Pan-Shun Lau (University of Nevada Reno) DTSTART:20210315T230000Z DTEND:20210315T235000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/5 DESCRIPTION:Title: The C-numerical Range of Matrices\nby Pan-Shun Lau (Universit y of Nevada Reno) as part of 2021 UNR Spring Matrix Seminar\n\nAbstract: T BA\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Huajun Huang (Auburn University) DTSTART:20210322T230000Z DTEND:20210322T235000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/6 DESCRIPTION:Title: Trace Preserving Properties and Invertible Completely Positive Ma ps\nby Huajun Huang (Auburn University) as part of 2021 UNR Spring Mat rix Seminar\n\n\nAbstract\nWe describe maps $\\phi_1\,\\ldots\,\\phi_m$ be tween various matrix spaces that satisfy the trace preserving properties $ Tr(\\phi_1(A_1)\\cdots\\phi_m(A_m))=Tr(A_1\\cdots A_m)$\, and explore the connection of this problem to invertible completely positive maps in quant um information theory\, which could be used in quantum decoding and quantu m error correction.\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis Verde (Metropolitan Autonomous University) DTSTART:20210329T230000Z DTEND:20210329T235000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/7 DESCRIPTION:Title: Matrices of coefficients of hypergeometric orthogonal polynomial 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 polyno mials 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 an infin ite lower triangular invertible matrix.\nAn important problem in the theor y of orthogonal polynomial sequences is the following:\n\nFind $v_k(t)$ an d $C$ such that the polynomials $u_k(t)$ satisfy a three-term recurrence r elation 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 certain ge neralized 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 sequence o f nodes that is linearly recurrent.\nThe main step is proving that certain matrix that is constructed using $C$\, $C^{-1}$\, and a pair of sequen ces\, is tridiagonal.\n\nOur construction produces all the hypergeometric and basic hypergeometric orthogonal polynomial families.\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kijti Rodtes (Naresuan University) DTSTART:20210405T230000Z DTEND:20210405T235000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/8 DESCRIPTION:Title: Multinomial Vandermonde Convolution via Permanent\nby Kijti R odtes (Naresuan University) as part of 2021 UNR Spring Matrix Seminar\n\n\ nAbstract\nIn this talk\, a generalized Laplace expansion for the permanen t function will be provided. As a consequence\, a multinomial Vandermonde convolution can be reproved. Also\, some combinatorial identities are al so discussed by applying special matrices to the expansion.\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Mehmet Gumus (University of Nevada Reno) DTSTART:20210412T230000Z DTEND:20210412T235000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/9 DESCRIPTION:Title: Some New Results on Positive Semi-Denite Block Matrices\nby M ehmet Gumus (University of Nevada Reno) as part of 2021 UNR Spring Matrix Seminar\n\n\nAbstract\nIn this talk\, we will present several recent devel opments on positive semi-definite block matrices. We will consider the nor m inequalities\, the trace inequalities\, and a characterization for some special types of positive partial transpose matrices. Several open problem s will also be discussed.\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Kuo-Zhong Wang (National Chiao Tung University) DTSTART:20210419T230000Z DTEND:20210419T235000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/10 DESCRIPTION:Title: Numerical ranges of matrix powers\nby Kuo-Zhong Wang (Nation al Chiao Tung University) as part of 2021 UNR Spring Matrix Seminar\n\n\nA bstract\nFor any $n$-by-$n$ complex matrix $A$\, its numerical range $W(A) $ is defined by $\\{x^*Ax:x\\in \\mathbb{C}^n\,x^*x=1\\}$. The study of th e numerical range has a history of one hundred years now. It started with the amazing result of Toeplitz-Hausdorff that the numerical range is alway s a convex set in the plane. $W(A)$ is a set that can be used to learn som ething about the matrix $A$\, and it can often give information that the s pectrum alone cannot give. In this talk\, we start to present some basic p roperties of the numerical range of a matrix. Then we will introduce some recent results and problems on this topic.\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Yongdo Lim (Sungkyunkwan University) DTSTART:20210426T230000Z DTEND:20210426T235000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/11 DESCRIPTION:Title: The Karcher mean of $2\\times 2$ triples\nby Yongdo Lim (Sun gkyunkwan University) as part of 2021 UNR Spring Matrix Seminar\n\n\nAbstr act\nA long-standing open problem for the Karcher (alternatively\, Riemann ian 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 mean for $2 \\times 2$ triples.\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Frank Hall (Georgia State University) DTSTART:20210503T230000Z DTEND:20210503T235000Z DTSTAMP:20260422T225658Z UID:UNRMatrixSeminar/12 DESCRIPTION:Title: G-matrices\, J-orthogonal matrices\, and their sign patterns \nby Frank Hall (Georgia State University) as part of 2021 UNR Spring Matr ix Seminar\n\n\nAbstract\nA real matrix $A$ is a G-matrix if $A$ is nonsin gular and there exist nonsingular diagonal matrices $D_1$ and $D_2$ such t hat\n$A^{-T}= D_1 AD_2$\, where $A^{-T}$ denotes the transpose of the inve rse of $A$.\nDenote by $J = {\\rm diag}(\\pm 1)$ a diagonal (signature) ma trix\, each of whose diagonal entries is $+1$ or $-1$. A nonsingular 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 ta lk\, many connections are made between these two types of matrices. \nIn p articular\, a matrix $A$ is a G-matrix if and only if $A$ is diagonally (w ith positive diagonals) equivalent to a column (or row) permutation of a \ nJ-orthogonal matrix. An investigation into the sign patterns of these mat rices is explored. It is observed that the sign patterns of the G-matrices are \nexactly the permutation equivalences of the sign patterns of the J- orthogonal matrices.\n\nSign potentially J-orthogonal conditions are also considered. Some open questions are presented and continuing work is discu ssed. \nThis research is joint with several authors including Miroslav Fie dler and Miro Rozloznik of the Czech Academy of Sciences.\n LOCATION:https://researchseminars.org/talk/UNRMatrixSeminar/12/ END:VEVENT END:VCALENDAR