The tracial moment problem and trace-optimization of polynomials
نویسندگان
چکیده
منابع مشابه
The tracial moment problem and trace-optimization of polynomials
The main topic addressed in this paper is trace-optimization of polynomials in noncommuting (nc) variables: given an nc polynomial f , what is the smallest trace f(A) can attain for a tuple of matrices A? A relaxation using semidefinite programming (SDP) based on sums of hermitian squares and commutators is proposed. While this relaxation is not always exact, it gives effectively computable bou...
متن کاملTrace-positive polynomials, sums of hermitian squares and the tracial moment problem
A polynomial f in non-commuting variables is trace-positive if the trace of f(A) is positive for all tuples A of symmetric matrices of the same size. The investigation of trace-positive polynomials and of the question of when they can be written as a sum of hermitian squares and commutators of polynomials are motivated by their connection to two famous conjectures: The BMV conjecture from stati...
متن کاملThe Truncated Tracial Moment Problem
We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a tracial sequence. We prove that such a sequence can be represented with tracial moments of matrices if its corresponding moment matrix is positive semidefini...
متن کاملTrace-positive polynomials and the quartic tracial moment problem Polynômes avec une trace positive et le problème quartique des moments traciaux
The tracial analog of Hilbert’s classical result on positive binary quartics is presented: a trace-positive bivariate noncommutative polynomial of degree at most four is a sum of hermitian squares and commutators. This is applied via duality to investigate the truncated tracial moment problem: a sequence of real numbers indexed by words of degree four in two noncommuting variables with values i...
متن کاملthe problem of divine hiddenness
این رساله به مساله احتجاب الهی و مشکلات برهان مبتنی بر این مساله میپردازد. مساله احتجاب الهی مساله ای به قدمت ادیان است که به طور خاصی در مورد ادیان ابراهیمی اهمیت پیدا میکند. در ادیان ابراهیمی با توجه به تعالی خداوند و در عین حال خالقیت و حضور او و سخن گفتن و ارتباط شهودی او با بعضی از انسانهای ساکن زمین مساله ای پدید میاید با پرسشهایی از قبیل اینکه چرا ارتباط مستقیم ویا حداقل ارتباط وافی به ب...
15 صفحه اولذخیره 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: Mathematical Programming
سال: 2011
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-011-0505-8