1-3 of 3 results
-
Matrix Analysis and Operator Theory
PI Edward Poon
Matrices and operators are ubiquitous throughout science, engineering, and mathematics; they are the transformations that arise whenever one studies a linear system (or approximates a nonlinear system by a linear one). Examples include rotations and reflections (rigid motions of space), spin operators (quantum mechanics and quantum computing), stress tensors (mechanics), regression and curve fitting (statistics and data analysis), derivatives and linear differential operators (dynamical systems), to name just a few. By studying various properties, relations, and transformations of matrices and operators one may obtain insight into a wide range of phenomena.
Read moreCategories: Faculty-Staff
-
Analyticity and kernel stabilization of unbounded derivations on C*-algebras
We first show that a derivation studied recently by E. Christensen has a set of analytic elements which is strong operator topology-dense in the algebra of bounded operators on a Hilbert space, which strengthens a result of Christensen. Our second main result shows that this derivation has kernel stabilization, that is, no elements have derivative eventually equal to 0 unless their first derivative is 0. As applications, we (1) show that a family of derivations on C*-algebras studied by Bratteli and Robinson has kernel stabilization, and (2) we provide sufficient conditions for when two operators which satisfy the Heisenberg Commutation Relation must both be unbounded.
Read moreCategories: Faculty-Staff
-
Simulation Based Inquiry Oriented Linear Algebra
CO-I Ashish Amresh
Games that teach introductory concepts in linear algebra such as vectors, span and dependence are created to be used by instructors in an undergraduate class.
Read moreCategories: Faculty-Staff
1-3 of 3 results