Non-Archimedean Views on Gershgorin’s Theorem and Diagonal Dominance

Abstract

Classical matrix theory works over the complex numbers; its reliance on the usual absolute value makes it an Archimedean theory. In this paper, we consider non-Archimedean counterparts of the Gershgorin disk theorem and diagonally dominant matrices. We compare and contrast the Archimedean and non-Archimedean contexts. A remarkable dissimilarity is that diagonally dominant matrices enjoy more structure in the non-Archimedean setting.

MSC::

• 15A18
• 15A42
• 12J25

Additional information

Notes on contributors

Bogdan Nica

Bogdan Nica received his Ph.D. from Vanderbilt University. After temporary positions at the University of Victoria in Canada, Göttingen University in Germany, and McGill University in Canada, he joined IUPUI in 2020. He currently enjoys meeting his colleagues and students in person.

Dacota Sprague

Dacota Sprague is an undergraduate of IUPUI. He is pursuing a bachelor’s in pure mathematics, and his end goal is to work alongside his fellow mathematics professors as a professor himself.