27th Conference of the International Linear Algebra Society (ILAS 2026)

Sign patterns that require or allow the non-symmetric strong spectral property

May 19, 2026, 2:00 PM

25m

Goodwin Hall 155 (Virginia Tech)

Minisymposium Talk The Inverse Eigenvalue Problem of a Graph and Zero Forcing The Inverse Eigenvalue Problem of a Graph and Zero Forcing

Speaker

Kevin Vander Meulen (Redeemer University)

Description

A matrix $A$ has the non-symmetric strong spectral property (nSSP) if $X=O$ is the only matrix which satisfies $A\circ X=O$ and $AX^T=X^TA$. This property comes with implications for eigenvalue properties of sign patterns, including a bifurcation lemma and superpattern lemma. We describe some classes of sign patterns for which every matrix with the sign pattern will have the nSSP. We also provide methods for recognizing when a sign pattern restricts matrices from having the nSSP. In particular, we provide a characterization of the sign patterns that allow a matrix with the nSSP. This presentation is based on joint work with Michael Cavers and Zhongshan Li.