DDVV-type inequality for Hermitian matrices

Refinements of Kantorovich Inequality for Hermitian Matrices

a cauchy-schwarz type inequality for fuzzy integrals

نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.

Sums of random Hermitian matrices and an inequality by Rudelson

i=1 ǫiAi (1) of deterministic Hermitian matrices A1, . . . , An multiplied by random coefficients. Recall that a Rademacher sequence is a sequence {ǫi}i=1 of i.i.d. random variables with ǫ1 uniform over {−1,+1}. A standard Gaussian sequence is a sequence i.i.d. standard Gaussian random variables. Our main goal is to prove the following result. Theorem 1 (proven in Section 3) Given positive inte...

Congruence of Hermitian Matrices by Hermitian Matrices

Two Hermitian matrices A, B ∈ Mn(C) are said to be Hermitian-congruent if there exists a nonsingular Hermitian matrix C ∈ Mn(C) such that B = CAC. In this paper, we give necessary and sufficient conditions for two nonsingular simultaneously unitarily diagonalizable Hermitian matrices A and B to be Hermitian-congruent. Moreover, when A and B are Hermitian-congruent, we describe the possible iner...

A Ddvv Inequality for Submanifolds of Warped Products

We prove a DDVV inequality for submanifolds of warped products of the form I ×a Mn(c) where I is an interval and Mn(c) a real space form of curvature c . As an application, we give a rigidity result for submanifolds of R×eλt Hn(c). RÉSUMÉ. Une inégalité de type DDVV pour les sous-variétés des produits tordus. Nous donnons une inégalité de type DDVV pour les sous-variétés des produits tordus de ...