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

A Graphical Approach to Isospectral Unfoldings

May 21, 2026, 3:15 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

Dallin Seyfried (Brigham Young University)

Description

An isospectral reduction is a method of shrinking a large matrix into a smaller matrix while preserving properties of the original's spectrum. The inverse, an isospectral unfolding, takes a matrix of an isospectral reduction and expands it into a larger matrix that has that reduction. We present a system of nonlinear equations forming the foundation of general isospectral unfolding. Graphs naturally tie in to isospectral reductions via their adjacency matrices. Thus, automorphic orbits, equitable partitions, and their relations to graphs sharing the same isospectral reductions will be explored, theorems given, and proofs discussed. Connections to quantum walk matrices will also be made.