# Almost Commuting Matrices

## Document Type

Presentation Abstract

## Presentation Date

11-18-2019

## Abstract

Suppose that A and B are square matrices of the same size that do not commute, but *almost* commute. That is, AB and BA are not equal but *close* to equal. To what extent can A and B be approximated by matrices that commute exactly? We will survey a variety of known results to variations of this problem, both positive and negative. Much of the discussion will be elementary, but we will also draw connections to the winding number of the punctured plane and to lifting problems for C*-algebras and K-theory obstructions.

## Recommended Citation

Boersema, Jeff, "Almost Commuting Matrices" (2019). *Colloquia of the Department of Mathematical Sciences*. 574.

https://scholarworks.umt.edu/mathcolloquia/574

## Additional Details

Monday, November 18, 2019 at 3:00 p.m. in Math 103

Refreshments at 4:00 p.m. in Math Lounge 109