Rearrangement and matrix product inequalities
نویسندگان
چکیده
منابع مشابه
Some Matrix Rearrangement Inequalities
We investigate a rearrangement inequality for pairs of n × n matrices: Let ‖A‖p denote (Tr(A∗A)p/2)1/p, the C trace norm of an n×n matrix A. Consider the quantity ‖A+B‖p+‖A−B‖p. Under certain positivity conditions, we show that this is nonincreasing for a natural “rearrangement” of the matrices A and B when 1 ≤ p ≤ 2. We conjecture that this is true in general, without any restrictions on A and...
متن کاملRelative rearrangement and interpolation inequalities
We prove here that the Poincaré-Sobolev pointwise inequalities for the relative rearrangement can be considered as the root of a great number of inequalities in various sets not necessarily vector spaces. In particular, new interpolation inequalities can be derived. Reordenamiento relativo y desigualdades de interpolación Resumen. Mostramos que las desigualdades puntuales de Poincaré-Sobolev pa...
متن کاملInequalities for the ’ h c e of Matrix Product
It is proved in this note that all Hurwitz polynomials of ordernot less than n form two simply connected Bore1 cones in the polynomialparameter space. Based on this result, edge theoremsfor Hurwitz sta-bility of general polyhedrons of polynomials and boundary theorems forHurwitz stability of compact sets of polynomials are obtained. Both casesof families of polynomials w...
متن کاملMatrix and Operator Inequalities
In this paper we prove certain inequalities involving matrices and operators on Hilbert spaces. In particular inequalities involving the trace and the determinant of the product of certain positive definite matrices.
متن کاملA Short Course on Rearrangement Inequalities
These notes grew out of introductory courses for graduate students that I gave at the First IMDEA Winter School in Madrid in January 2009, and at the Università di Napoli “Federico II” in April 2009. The manuscript has been been slightly expanded to five sections, each providing material for one or two hours of lecture. The first section gives an overview of the classical rearrangement inequali...
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: Linear Algebra and its Applications
سال: 1990
ISSN: 0024-3795
DOI: 10.1016/0024-3795(90)90227-4