On invertible nonnegative Hamiltonian operator matrices
Guohai Jin, Guolin Hou, Alatancang Chen, and Deyu Wu
TL;DR
This paper provides new characterizations and conditions for invertibility of nonnegative Hamiltonian operator matrices, utilizing a novel proof method based on connections with Pauli matrices, advancing theoretical understanding in operator theory.
Contribution
It introduces new characterizations and necessary and sufficient conditions for invertibility, unifying and extending previous results through a novel proof approach.
Findings
New characterizations of nonnegative Hamiltonian matrices
Necessary and sufficient conditions for invertibility
Connections between Pauli matrices and Hamiltonian matrices
Abstract
Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operators to be invertible are obtained; so that the main results in the previously published papers are corollaries of the new theorems. Most of all we want to stress the method of proof. It is based on the connections between Pauli operator matrices and nonnegative Hamiltonian matrices.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics · Matrix Theory and Algorithms · Holomorphic and Operator Theory