منابع مشابه
Notes on super-operator norms induced by schatten norms
Let Φ be a super-operator, i.e., a linear mapping of the form Φ : L(F) → L(G) for finite dimensional Hilbert spaces F and G. This paper considers basic properties of the super-operator norms defined by ‖Φ‖q→p = sup{‖Φ(X)‖p/‖X‖q : X 6= 0}, induced by Schatten norms for 1 ≤ p, q ≤ ∞. These super-operator norms arise in various contexts in the study of quantum information. In this paper it is prov...
متن کاملSchatten norms of Toeplitz matrices with Fisher-Hartwig singularities
The asymptotics of the Schatten norms of finite Toeplitz matrices generated by functions with a Fisher-Hartwig singularity are described as the matrix dimension n goes to infinity. The message of the paper is to reveal some kind of a kink: the pth Schatten norm increases as n to the power 1/p before the singularity reaches a critical point and as n to an exponent depending on the singularity be...
متن کاملEmbeddings of Schatten Norms with Applications to Data Streams
Given an n×d matrix A, its Schatten-p norm, p ≥ 1, is defined as ‖A‖p = (∑rank(A) i=1 σi(A) p )1/p , where σi(A) is the i-th largest singular value of A. These norms have been studied in functional analysis in the context of non-commutative `p-spaces, and recently in data stream and linear sketching models of computation. Basic questions on the relations between these norms, such as their embed...
متن کاملThe balanced truncation error bound in Schatten norms
The first main result in this article provides an error bound for balanced truncation where the matrix norm used is a general Schatten norm rather than the usual operator norm. The second main result in this article is that for the Schatten 1-norm (the trace class norm) this bound, for systems with a semi-definite Hankel operator, is in fact an equality. This class of systems for which we obtai...
متن کاملUnified Scalable Equivalent Formulations for Schatten Quasi-Norms
The Schatten quasi-norm can be used to bridge the gap between the nuclear norm and rank function. However, most existing algorithms are too slow or even impractical for large-scale problems, due to the singular value decomposition (SVD) or eigenvalue decomposition (EVD) of the whole matrix in each iteration. In this paper, we rigorously prove that for any 0< p≤ 1, p1, p2 > 0 satisfying 1/p= 1/p...
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: 2020
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/15179