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# Linear Algebra

DMS Linear Algebra/Algebra Seminar
Oct 10, 2017 04:00 PM
Parker Hall 356

Speaker: Reimbay Reimbayev

Title: Synchronization in Neuronal Networks and more

Abstract: Synchronized neuronal firing is notoriously known to induce pathological brain states, such as epilepsy and Parkinson’s tremors. In this talk I will present my recent work published in PTRS. Using bifurcation theory and numerical simulations, I show why facilitating inhibition in a neuronal network might sometimes be counterproductive. I will also discuss a particular problem I have been interested from Graph Theory.

DMS Linear Algebar/Algebra Seminar
Oct 03, 2017 04:00 PM
Parker Hall 356

Speaker: Sunil Hans

Title: Annulus containing all the zeros of a polynomial

Abstract: As we know the properties of polynomials have been studied since the time of Gauss and Cauchy, and have played an important role in many scientific disciplines. Problems involving location of their zeros find important applications in many areas of applied mathematics. Since Abel and Ruffini proved that there is no general algebraic solution to polynomial equations of degree five or higher, the problem of finding an annulus containing all the zeros of a polynomial became much more interesting and over a period large number of results have provided in this direction.

This talk will introduce the new explicit bounds for the moduli of the zeros involving binomial coefficients, Fibonacci Numbers, Pell Numbers, Lucas Numbers and many more.

DMS Linear Algebra/Algebra Seminar
Sep 26, 2017 04:00 PM
Parker Hall 356

Speaker: Xavier Martínez-Rivera

Title: A new principal rank characteristic sequence

DMS Linear Algebra/Algebra Seminar
Sep 19, 2017 04:00 PM
Parker Hall 356

Speaker: Doug Leonard

Title: Desingularizing function fields

Abstract: I'll give a few examples of poorly coordinatized domains (and hence their function fields), and explain desingularization in terms of proper coordinatization and formal Laurent series. But, for a mostly linear algebra audience, I'll focus on what I call unimodular transformations (since they come from unimodular matrices), and how they do a better job of desingularization than sequences of blowups.

DMS Linear Algebra/Algebra Seminar
Sep 12, 2017 04:00 PM
Parker Hall 356

Speaker: Samir Raouafi

Title: On Pseudospectra and Norm Behavior of Matrices

Abstract: Eigenvalues are a useful tool for studying normal matrices.

Their eigenvectors can be taken to be orthogonal, and then they can be unitarily diagonalized. In contrast, non-normal matrices lack an orthogonal basis of eigenvectors. Thus, additional tools such as the numerical range and the pseudospectra are interesting for analyzing them.

This talk will introduce the theory of pseudospectra and discuss the norm behavior of matrices that have identical and super-identical pseudospectra.

DMS Linear Algebra/Algebra Seminar
Sep 05, 2017 04:00 PM
Parker Hall 356

Speaker: Xavier Martínez-Rivera

Title: A new principal rank characteristic sequence

DMS Linear Algebra/Algebra Seminar
Aug 29, 2017 04:00 PM
Parker Hall 356

Speaker: T.-Y. Tam

Title: Generalized numerical range: history and questions

Abstract: We will give a history of the development of the generalized numerical range in the context of Lie Theory including some important results. Geometric favor will be emphasized. We will also discuss some open questions.

Linear Algebra/Algebra Seminar
Jun 27, 2017 04:00 PM
Parker Hall 228

Speaker: Xavier Martínez-Rivera (Iowa State University)

Title: Principal rank characteristic sequences

Abstract: The necessity to know certain information about the principal minors of a given/desired matrix is a situation that arises in several areas of mathematics. As a result, researchers associated two sequences with an $$n \times n$$ symmetric, complex Hermitian, or skew-Hermitian matrix $$B$$. The first of these is the principal rank characteristic sequence (abbreviated pr-sequence). This sequence is defined as $$r_0]r_1 \cdots r_n$$, where, for $$k \geq 1$$, $$r_k = 1$$ if $$B$$ has a nonzero order-$$k$$ principal minor, and $$r_k = 0$$, otherwise; $$r_0 = 1$$ if and only if $$B$$ has a $$0$$ diagonal entry. The second sequence, one that enhances'' the pr-sequence, is the enhanced principal rank characteristic sequence (epr-sequence), denoted by $$\ell_1 \ell_2 \cdots \ell_n$$, where $$\ell_k$$ is either $$\tt A$$, $$\tt S$$, or $$\tt N$$, based on whether all, some but not all, or none of the order-$$k$$ principal minors of $$B$$ are nonzero.

In this talk, known results about pr- and epr-sequences are discussed. New restrictions for the attainability of epr-sequences by real symmetric matrices are presented. Particular attention will be paid to the epr-sequences that are attainable by symmetric matrices over fields of characteristic $$2$$: for the prime field of order $$2$$, a complete characterization of these epr-sequences is given.

Linear Algebra Seminar
Apr 18, 2017 04:00 PM
Parker Hall 246

Speaker: Huajun Huang

Title: Majorization, CMJD, and Kostant's pre-order

Abstract: Many majorization relations in matrix theory can be reinterpreted in terms of Kostant's pre-order on real semisimple Lie groups.  We introduce Kostant's pre-order and discuss some corresponding results in matrix theory and Lie theory. These involve the relations of singular values, eigenvalues, a-components, and the diagonal of a matrix, and some famous matrix inequalities.
Linear Algebra Seminar
Apr 11, 2017 04:00 PM
Parker Hall 246

Speaker: Zhouheng He

Title: Some new developments of Sylvester-type matrix equations

Abstract: In this talk, we consider some systems of coupled Sylvester-type matrix equations. We give some necessary and sufficient solvability conditions for some systems of coupled Sylvester-type matrix equations in terms of ranks and generalized inverses of matrices. We also derive the general solutions to these systems when they are solvable.

Last Updated: 08/21/2017