A complex Gap lemma
نویسندگان
چکیده
منابع مشابه
A simple proof of Zariski's Lemma
Our aim in this very short note is to show that the proof of the following well-known fundamental lemma of Zariski follows from an argument similar to the proof of the fact that the rational field $mathbb{Q}$ is not a finitely generated $mathbb{Z}$-algebra.
متن کاملSimple proof of the detectability lemma and spectral gap amplification
The detectability lemma is a useful tool for probing the structure of gapped ground states of frustration-free Hamiltonians of lattice spin models. The lemma provides an estimate on the error incurred by approximating the ground space projector with a product of local projectors. We provide a simpler proof for the detectability lemma which applies to an arbitrary ordering of the local projector...
متن کاملA simple proof of the detectability lemma and spectral gap amplification
The detectability lemma is a useful tool for probing the structure of gapped ground states of frustration-free Hamiltonians of lattice spin models. The lemma provides an estimate on the error incurred by approximating the ground space projector with a product of local projectors. We provide a new, simpler proof for the detectability lemma which applies to an arbitrary ordering of the local proj...
متن کاملA Discrete Farkas Lemma
Given A ∈ Zm×n and b ∈ Zm, we consider the issue of existence of a nonnegative integral solution x ∈ Nn to the system of linear equations Ax = b. We provide a discrete and explicit analogue of the celebrated Farkas lemma for linear systems in Rn and prove that checking existence of integral solutions reduces to solving an explicit linear programming problem of fixed dimension, known in advance.
متن کاملA splitting lemma
In this paper, we study the relations between the numerical structure of the optimal solutions of a convex programming problem defined on the edge set of a simple graph and the stability number (i.e. the maximum size of a subset of pairwise non-adjacent vertices) of the graph. Our analysis shows that the stability number of every graph G can be decomposed in the sum of the stability number of a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2019
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14716