Presentation Title

What is the boundary of a finite subset of the pac-man universe?

Advisor Information

Patrick X. Rault

Presentation Type

Poster

Start Date

26-3-2021 12:00 AM

End Date

26-3-2021 12:00 AM

Abstract

Given a square matrix A, its numerical range is the image of a certain map gA from the unit sphere to the complex plane. This numerical range is the convex hull of a “boundary generating curve”. It is useful in the theory of linear algebra in approximating eigenvalues, and has applications in quantum computing. In the modular situation of finite fields, which resembles the universe in the game pac-man where there is no concept of boundary, the aforementioned boundary generating curve has some very special properties. If A is a 2-by-2 matrix, then gA is a two-to-one map (up to trivial multiples), except on the boundary generating curve, where it is a one-to-one map (up to trivial multiples). We will discuss the geometry of the image of gA (the numerical range of A) using this boundary generating curve.

Additional Information (Optional)

Unavailable 12:30pm-5:00pm US Central due to work.

This document is currently not available here.

COinS
 
Mar 26th, 12:00 AM Mar 26th, 12:00 AM

What is the boundary of a finite subset of the pac-man universe?

Given a square matrix A, its numerical range is the image of a certain map gA from the unit sphere to the complex plane. This numerical range is the convex hull of a “boundary generating curve”. It is useful in the theory of linear algebra in approximating eigenvalues, and has applications in quantum computing. In the modular situation of finite fields, which resembles the universe in the game pac-man where there is no concept of boundary, the aforementioned boundary generating curve has some very special properties. If A is a 2-by-2 matrix, then gA is a two-to-one map (up to trivial multiples), except on the boundary generating curve, where it is a one-to-one map (up to trivial multiples). We will discuss the geometry of the image of gA (the numerical range of A) using this boundary generating curve.