Posts tagged: linear algebra

What is the minimum number of links that you need to connect 4 computers in a wired network? 3.

Let's say we have a graph (i.e. network), and we want to cluster the vertices (nodes).  Here, think of the nodes as people, agents, oscillators, some dynamic being, and the edges... the edges tell...

It always excites me when I see a combinatorial matrix theory problem, and this is no exception, though it is so basic that it shows up in all forms and shapes. Let me start with a combinatorial...

This past summer I was given a course in introductory linear algebra to teach. The topics of the course, as usual, start from solving systems of linear equations, and then matrices, determinant and...

In a huge graph, it is hard to determine a bottleneck by just looking at it, or doing any type of search. And by a bottleneck, I mean part of graph that is not very much connected to the other part....

My first solo paper "Existence of a Not Necessarily Symmetric Matrix with Given Distinct Eigenvalues and Graph" got published in Journal of Linear Algebra and its Applications, yesterday. It took it...

Today I started my linear algebra class by motivating the determinant using a little bit of history and applications. In particular I talked about determinant appearing in the change of variables in...

One of the things that I always tell my students is to check their solutions when they are done solving a problem. That by itself can mean several things, depending on what the problems is. Of course...

I've been using sage for a while now. I've also been teaching linear algebra for a few years. One of the problems in teaching linear algebra is coming up with a handful of examples of matrices that...

Gershgorin circle theorem roughly states that the eigenvalues of an $n \times n$ matrix lie inside $n$ circles where $i$-th circle is centred at $A{i,i}$ and its radius is the sum of the absolute...

We started the project in Graduate Research Workshop in Combinatorics (Rocky Mountain Great Plains GRWC) in summer 2014, hosted by University of Denver and University of Colorado Denver. Two weeks of...

In Theorem 3.1 of "The combinatorial inverse eigenvalue problems: complete graphs and small graphs with strict inequality, W. Barrett, A. Lazenby, N. Malloy, C. Nelson, W. Sexton, Electronic Journal...

If you know about my work, you know that for the past several years I've been working on a special type of problems called structured inverse eigenvalue problems (or SIEP's for short). Well, I mainly...

I went to several talks and meetings in the past few days, and I am going to talk about some of them, but first let me start with some predicting game:

Ehssan Khanmohammadi and I just submitted a paper on inverse eigenvalue problems for infinite graphs. Essentially we proved that for a given bounded set $\Lambda$ and an infinite graph $G$ on...

Today I read a lot of random mathematics and many of them led to places outside math, and among them is this one: Parkinson's Law. One of them that at this last hour of work day is still related to...

For the past several months my Saturdays consist of two meetings, each of which about 4 hours long, with two of my colleagues working on various problems. Clearly we've hit a lot of dead ends, and...

We (Sudipta Mallik and I) just submitted our paper on the "Spectral characterization of matchings in graphs". It is based on our previous work on "Construction of real skew-symmetric matrices from...

30 pages for the new paper. Almost done.

Gilbert Strang talking about his favorite topic at the Joint Math Meeting 2014, Baltimore, MD.

> Permanent & Determinant: Non-identical Twins > Tuesday, May 20, 2014 > > The determinant is undoubtedly the most important polynomial function in mathematics. Its lesser known sibling, the...

Algebra, Combinatorics, and Number Theory Seminar Ross Hall 247 3:10pm, Tuesday, 29 April 2014