Parametrising spectrahedra

Martin Helsø, Mathematics

Poster abstract

A matrix is a table of numbers, with rules for adding and multiplying such tables with each other. To a matrix, we can associate a set of important numbers called eigenvalues. These reflect the underlying geometric action of the matrix.

In our work, we study convex bodies of symmetric matrices where all the eigenvalues are nonnegative. These bodies are called spectrahedra. Spectrahedra appear naturally in applied fields such as optimisation and statistics. We consider only matrices with four rows and four columns. In this case, we describe the subset of spectrahedra that have a boundary that can be parametrised by a class of simple functions.

This is joint work with Kristian Ranestad.

Published May 19, 2017 10:57 AM - Last modified May 19, 2017 10:57 AM