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# Linear Algebra

DMS Linear Algebra/Algebra Seminar
Nov 27, 2018 04:00 PM
Parker Hall 354

Speaker:  Xavier Martinez-Rivera

Title:  The qpr-sequence

DMS Linear Algebra/Algebra Seminar
Nov 13, 2018 04:00 PM
Parker Hall 354

Speaker: Mehmet Gumus

Title: On Simultaneous Lyapunov Diagonal Stability

DMS Linear Algebra/Algebra Seminar
Nov 06, 2018 04:00 PM
Parker Hal 354

Speaker: Zhen-hua Lyu

Title: An extremal problem on 0-1 matrices

Abstract: Let $$n$$ and $$k$$ be positive integers. If both $$A$$ and $$A^k$$ are 0-1 matrices, what's the maximum number of ones in $$A$$? In this talk, the known results will be shown and a related problem will be discussed.

DMS Linear Algebra/Algebra Seminar
Oct 30, 2018 03:00 PM
Parker Hall 246

PLEASE NOTE CHANGE IN TIME AND PLACE

Speaker:  Sima Ahsani

Title:  Log-majorization Inequalities Involving Geometric Mean of Matrices

DMS Linear Algebra/Algebra Seminar
Oct 23, 2018 04:00 PM
Parker Hall 354

Speaker:  Samir Raouafi

Title:  Positive Semidefinite Block Matrices and Norm Inequalities

Abstract:  Positive semidefinite block matrices occur as an efficient tool in matrix analysis and quantum information theory. In particular, those partitioned in two by two blocks allow to derive a lot of important norm inequalities. Hiroshima's 2003 result, which provides a majorization criteria for distillability of a bipartite quantum state, sheds light on an interesting norm inequality in matrix analysis. In this talk, we will discuss some extension of this inequality. Furthermore, we will constructively provide a counter-example of Bourin--Lee--Lin's conjecture.

DMS Linear Algebra/Algebra Seminar
Oct 16, 2018 04:00 PM
Parker Hall 354

Speaker:  Xiaoji Liu

Title: Partial order of matrices and generalized inverse

Abstract: Many researchers in the field have paid much attention to minus-type partial orders, and have scored fruitful findings. Findings with respect to non-minus-type partial orders, though comparatively few, have greatly enriched the matrix partial order theory. We derive some characterizations of the C-N partial ordering, create a new partial ordering (the G-Drazin partial ordering) , and  by using the L¨owner partial order and the core partial order, we introduce a new partial order (the CL partial ordering) on the set of core matrices. We will present some results relating the Sharp ordering (a ≤♯ b) and investigate the properties of one-sided cyclic ideals generated by the group or Moore--Penrose invertible element in rings.  In the last section, we consider the following matrix inequality:  AXA<A  in the star, sharp and core partial orders, respectively.

DMS Linear Algebra/Algebra Seminar
Oct 09, 2018 04:00 PM
Parker Hall 354

Speaker:  Tin-Yau Tam

Title: The relation of a nonsingular matrix and its components in polar decomposition

Abstract: Each nonsingular matrix A has the so called polar decomposition A =  PU (or UP) where P is positive definite and U is unitary. The Weyl--Horn Theorem gives a nice relation between the eigenvalues of A and the eigenvalues of P. The relation is known as log majorization and is on the moduli of the eigenvalues of A and P. Kostant extended the result in the context of semisimple Lie groups. The Horn--Steinberg Theorem gives a nice relation between the eigenvalues of A and the eigenvalues of U. The relation is on the arguments of the eigenvalues A and the arguments of the eigenvalues of U. We will review these two theorems and provide some progress toward the extension of Horn--Steinberg Theorem in the context of complex semsimple Lie groups.

DMS Linear Algebra/Algebra Seminar
Oct 02, 2018 04:00 PM
Parker Hall 254

Speaker:  Huajun Huang

Title:  Upper triangular similarity, Belitskii's canonical form, and graphical algorithm

Abstract: I will give an up-to-date report on the upper triangular similarity of strictly upper triangular matrices. The Belitskii's algorithm leads to a Belitskii's canonical form for each upper triangular similarity orbit. I will explain how to use the double coset canonical form and graphical algorithm to determine Belitskii's canonical form efficiently. Some new results will be presented.

This work is joint with Meaza Bogale and Ming-Cheng Tsai.

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.

Last Updated: 08/21/2017