05C50 Online Seminar: Jephian Lin

  • Date: 12/09/2022
  • Time: 08:00
Jephian Lin, National Sun Yat-sen University (Taiwan)



Inverse eigenvalue problem for a graph


We often encounter matrices whose pattern (zero-nonzero, or sign) is known while the precise value of each entry is not clear. Thus, a natural question is what we can say about the spectral property of matrices of a given pattern. When the matrix is real and symmetric, one may use a simple graph to describe its off-diagonal nonzero support. For example, it is known that an irreducible tridiagonal matrix (whose pattern is described by a path) only allows eigenvalues of multiplicity one. In contrast, a periodic Jacobi matrix (whose pattern is described by a cycle) allows multiplicity two but no more. The inverse eigenvalue problem of a graph (IEPG) focuses on the matrices whose pattern is described by a given graph and studies their possible spectra. In this talk, we will go through some of the histories of the IEPG and see how combinatorial methods (zero forcing) and analytic methods (implicit function theorem) can come into play in modern-day research.


Stephen Kirkland, University of Manitoba

Hermie Monterde, University of Manitoba

Other Information: 

The 05C50 Online is an international seminar about graphs and matrices held twice a month on Fridays.


Time: 8AM Pacific/10AM Central 


For more information, visit https://sites.google.com/view/05c50online/home.


If you would like to attend, please register using this form to receive the zoom links: https://docs.google.com/forms/d/e/1FAIpQLSdQ98fh58cgeSWzbFe3t77i28FXDck1gYuX9jv_qd4kEf5l_Q/viewform?usp=sf_link