Degeneracy of eigenvalues and singular values of parameter dependent matrices

Applied and Computational Mathematics Seminar
Monday, May 6, 2024 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005 and
Alessandro Pugliese РUniversità degli Studi di Bari Aldo Moro Рalessandro.pugliese@uniba.it
Sung Ha Kang

Speaker will present in person.

Hermitian matrices have real eigenvalues and an orthonormal set of eigenvectors. Do smooth Hermitian matrix valued functions have smooth eigenvalues and eigenvectors? Starting from such question, we will first review known results on the smooth eigenvalue and singular values decompositions of matrices that depend on one or several parameters, and then focus on our contribution, which has been that of devising topological tools to detect and approximate parameters' values where eigenvalues or singular values of a matrix valued function are degenerate (i.e. repeated or zero).

The talk will be based on joint work with Luca Dieci (Georgia Tech) and Alessandra Papini (Univ. of Florence).