Convergent Gershgorin Disks Digital Print 2018

The cover art was inspired by the article in this issue by Melman. It imagines a series of $7\times 7$ similar matrices having full rank, where the Gershgorin disks become smaller and smaller, converging on the eigenvalues. Given a square $n \times n$ matrix $A$ of rank $n$, it can be diagonlized to a matrix $D$; thus the matrices $A$ and $D$ are similar. If one applies the Gershgorin circle theorem (GCT) to $D$, one will just get circles of radius 0 (thus points) at the eigenvalues. On the other hand, the GCT applied to $A$ will generally yield circles of various size containing the eigenvalues. Any matrix $B$ similar to $A$ (and $D$) will have the same eigenvalues, so the GCT applied to $B$ will give another set of circles around the eigenvalues.

Background and Inspiration

This work was originally done for use as cover art for the October 2018 issue of Mathematics Magazine. This is the nineteenth of 25 original artworks I created for the journal Mathematics Magazine during 2015–2019.

Publication History

• Mathematics Magazine, Cover Art, Vol. 91, No. 4, October 2018.