On March 26th 2026 at 17:00 in the FMI Conference Hall meeting of the FMI Colloquium will be held.
Prof. Hriso Sendov, Western University, London, Canada is going to give a research presentation on topic:
Aggregate Bounds on the eigenvalues of the principal submatrices of a Hermitian matrix and majorization relations
Abstract:
We extend bounds, proved by R.C. Thompson in 1966, on the sum of the j-th largest eigenvalues of the (n-1) х (n-1) principal matrices of an n х n Hermitian matrix. Our bounds are stronger than just summing up Thompson's bounds. We achieve the extensions as a corollary of a more general result giving bounds on the zeros of the generalized derivatives of polynomials with real roots. We use the extended bounds to obtain majorization relationships between the eigenvalues of all m х m principal matrices of an n х n Hermitian matrix. These majorization relationships imply both a well-known majorization result by Schur and the well-known Szasz's inequalities.
Prior to the presentation, colloquium participants are invited at 16:30 in the FMI Conference Hall for an informal discussion over coffee/tea.
You are welcome!