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# Algebra

DMS Linear Algebra/Algebra Seminar
Sep 25, 2018 04:00 PM
Parker Hall 354

Speaker: Douglas A. Leonard

Title:  Using Computer Algebra Systems to improve mathematical theory

Abstract:  Mathematicians seem adverse to putting examples in their research papers, higher level textbooks, or even course notes. (My intro to commutative algebra was a slick deﬁnition-theorem-proof course from which I learned nothing about the topic but something about proofs instead.) This is compounded when others write code to implement theory in some CAS (computer algebra system). Mathematical theory, can be wrong, misguided, too general, or too complicated. The code can be wrong, misguided, too general, or too complicated as well, even when the underlying math is at least not wrong. If one can work through reasonable examples of the theory (so non-trivial, but not hopelessly pathological) using a CAS, then one is forced to think very hard about programming each step. This can lead to alternative viewpoints and maybe even an overhauling of the theory. I’ll probably concentrate on resolving singularities, starting with the example described by $$y^3 + yx + x^5 = 0$$, using Macaulay2 and/or Singular.

DMS Linear Algebra/Algebra Seminar
Sep 18, 2018 04:00 PM
Parker Hall 354

Speaker:  Wei Gao

Title:  Inertia sets allowed or required by matrix patterns

Abstract:  A sign pattern matrix is a matrix whose entries come from the set $${+, -, 0}$$. A zero-nonzero pattern matrix is a matrix with entries from $${*,0}$$, where $$*$$ is nonzero.  Motivated by the possible onset of instability in dynamical systems, sign patterns and zero-nonzero patterns that allow or require some special sets of inertias and refined inertias are discussed in some papers. In this talk, some known results and techniques will be shown.

DMS Linear Algebra/Algebra Seminar
Sep 11, 2018 04:00 PM
Parker Hall 354

Speaker:  Sheng Bao

Title:  Metric spaces of abelian groups

Abstract:  Metric spaces arise as Cayley graphs of groups. In the locally finite infinite case, not much is known.  We consider metric spaces of vector groups (finitely generated torsion-free abelian groups) and propose some feasible questions about monotonicity of dimensions, finite resolution and bisectors while reporting on some beginning results on these.

DMS Linear Algebra / Algebra Seminar
Sep 04, 2018 04:00 PM
Parker Hall 354

Speaker: Daryl Granario

Title: The duality of the matrix transpose and conjugate-inverse maps

DMS Linear Algebra / Algebra Seminar
Aug 28, 2018 04:00 PM
Parker Hall 354

ORGANIZATIONAL MEETING

DMS Linear Algebra/Algebra Seminar
Apr 17, 2018 04:00 PM
Parker Hall 352

Speaker: Tin-Yau Tam

Title: Matrix Inequalities and Their Extensions to Lie Groups

Abstract: We will discuss some classical matrix inequalities and their extensions that are topics in my new book Matrix Inequalities and Their Extensions to Lie Groups.

DMS Linear Algebra/Algebra Seminar
Apr 03, 2018 04:00 PM
Parker Hall 352

Speaker: Avantha Indika

Title: A study of the structure of the symmetry classes

Abstract: Will discuss the studies on standard (decomposable) symmetrized tensors to understand the structure of symmetry classes of tensors associated with finite groups and the use of coset space to understand the geometric structure of a symmetry class of tensors.

DMS Linear Algebra/Algebra Seminar
Mar 20, 2018 04:00 PM

Speaker: Zejun Huang (Hunan University, China)

Title: Preserver problems on matrices

Abstract: Preserver problems on matrices concern the characterization of linear or nonlinear maps on matrices that leave certain properties invariant. In this talk, I will present some results on both linear and nonlinear preserver problems on matrices.

DMS Linear Algebra/Algebra Seminar
Mar 06, 2018 04:00 PM
Parker Hall 352

Speaker: Jason Liu

Title: Toeplitz Matrices, Symmetric Matrices, and Unitary Similarity

Abstract: In this talk, I will present the result that every Toeplitz matrix is uniformly unitarily similar to some complex symmetric matrices via a unitary matrix. Conversely, every symmetric matrix is unitarily similar to some Toeplitz matrix when $$n < 4$$.   I will relate this result with the facts of every matrix is a product of some Toeplitz matrices, which was proved by Ye and Lim in 2015, and a super-fast divide-and-conquer method to make the eigenproblem of Toeplitz matrices with nearly linear complexity presented by Vogel et al. in 2016. I will also present that every multilevel Toeplitz matrix is unitarily similar to a symmetric matrix.

DMS Linear Algebra/Algebra Seminar
Feb 27, 2018 04:00 PM
Parker Hall 352

Speaker: Zhuoheng He

Title: The general $$\phi$$-Hermitian solution to mixed pairs of quaternion matrix Sylvester equations

Abstract: In this talk, we consider two systems of mixed pairs of quaternion matrix Sylvester equations

$A_{1}X-YB_{1}=C_{1},~A_{2}Z-YB_{2}=C_{2}$ and $A_{1}X-YB_{1}=C_{1},~A_{2}Y-ZB_{2}=C_{2},$

where $$Z$$ is $$\phi$$-Hermitian. Some practical necessary and sufficient conditions for the existence of a solution $$(X,Y,Z)$$ to those systems in terms of the ranks and Moore-Penrose inverses of the given coefficient matrices will be presented. Moreover, the general solutions to these systems are explicitly given when they are solvable. We also provide some numerical examples to illustrate our results.

DMS Linear Algebra/Algebra Seminar
Feb 20, 2018 04:00 PM
Parker Hall 352

Speaker: Frank Uhlig

Title: The Eight Epochs of Math as regards past and future Matrix Computations

Abstract:  This survey paper gives a personal assessment of Epoch making advances in Matrix Computations, from antiquity and with an eye towards tomorrow.  It traces the development of number systems and elementary algebra and the uses of Gaussian Elimination methods from around 4000 BC on to current real-time Neural Network computations to solve time-varying matrix equations. The paper includes relevant advances from China from the 3rd century AD on and from India and Persia in the 9th and later centuries. Then it discusses the conceptual genesis of vectors and matrices in central Europe and in Japan in the 14th through 17th centuries AD. Followed by the 150 year cul-de-sac of polynomial root finder research for matrix eigenvalues, as well as the superbly useful matrix iterative methods and Francis’s matrix eigenvalue algorithm from the last century. Finally we explain the recent use of initial value problem solvers and high order 1-step ahead discretization formulas to master time-varying linear and nonlinear matrix equations via Zhang Neural Networks. This paper ends with a short outlook upon new hardware schemes with multilevel processors that go beyond the 0-1 base 2 framework which all of our past and current electronic computers have been using.

Last Updated: 01/20/2017