Réunion d'été SMC 2025
Ville de Québec, 6 - 9 juin 2025
Positivity: inequalities and preserving transformations
Org: Shaun Fallat (Regina) et Prateek Kumar Vishwakarma (Laval)
[PDF]
Org: Shaun Fallat (Regina) et Prateek Kumar Vishwakarma (Laval)
[PDF]
- SUJIT SAKHARAM DAMASE, Indian Institute of Science
- NATHANIEL JOHNSTON, Mount Allison University
The Factor Width and Factor Width Rank of a Matrix [PDF]
- NATHANIEL JOHNSTON, Mount Allison University
-
The "factor width" of a positive semidefinite matrix is the smallest positive integer k for which it can be written as a sum of positive semidefinite matrices that are each non-zero only in a single k-by-k principal submatrix. We explore numerous problems related to factor width, such as how we can bound it in terms of the matrix's eigenvalues, and we briefly describe some recently-discovered applications of this quantity in quantum information theory.
We also explore the "factor-width-k rank" of a matrix, which is the minimum number of rank-1 matrices that can be used in a matrix's factor-width-at-most-k decomposition. We show that the factor width rank of a banded or arrowhead matrix equals its usual rank, but for other matrices they can differ. We also establish several bounds on the factor width rank of a matrix, including a tight connection between factor-width-k rank and the k-clique covering number of a graph.
- POORNENDU KUMAR, University of Manitoba
- SARAH PLOSKER, Brandon University
- KARTIK SINGH, University of Waterloo
- MAXIMILIAN TORNES, University of Manitoba
Weighted composition operators on Hilbert function spaces on the ball [PDF]
- SARAH PLOSKER, Brandon University
-
A weighted composition operator on a reproducing kernel
Hilbert space (RKHS) is given by a composition, followed by a multiplication.
We characterize unitary and co-isometric weighted composition operators on
large class of RKHS of holomorphic functions on the Euclidean unit ball of $\mathbb{C}^n$. This
extends results of Martín, Mas and Vukotić from the disc to the ball. This is joint work with Michael Hartz.
- PRATEEK KUMAR VISHWAKARMA, Université Laval