- 18 Nov 2022
Lezione inaugurale del Dottorato in Matematica 38 ciclo. Functions of matrices: theory, applications and computation
In this talk I will first give a brief history of matrix and operator functions.
The story begins with the early work of Cayley and Sylvester on matrix algebra in the
XIX Century, continues in the XX Century with the important contributions of Weyr,
E. Cartan, Giorgi, and Cipolla, and culminates with the development of various functional
calculi for linear operators (both bounded and unbounded) in the context of modern
functional analysis. Much of this work is motivated by applications, especially in Physics,
a few of which will be described in the second part of the talk, together with emerging
new applications in Network Science. In the last part of the talk I will discuss some results
on decay properties of functions of large, sparse matrices and current work on efficient
algorithms for evaluating quantities such as the trace of a matrix function or the action of
a matrix function on a given vector using Krylov subspace methods.