Some matrix inequalities related to $J_{S^-}$ normal matrices
نویسندگان
چکیده
منابع مشابه
extensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولOn some matrix inequalities
The arithmetic-geometric mean inequality for singular values due to Bhatia and Kittaneh says that 2sj(AB ∗) ≤ sj(A∗A + B∗B), j = 1, 2, . . . for any matrices A,B. We first give new proofs of this inequality and its equivalent form. Then we use it to prove the following trace inequality: Let A0 be a positive definite matrix and A1, . . . , Ak be positive semidefinite matrices. Then tr k ∑
متن کاملSome 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 کاملCartesian decomposition of matrices and some norm inequalities
Let X be an n-square complex matrix with the Cartesian decomposition X = A + i B, where A and B are n times n Hermitian matrices. It is known that $Vert X Vert_p^2 leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)$, where $p geq 2$ and $Vert . Vert_p$ is the Schatten p-norm. In this paper, this inequality and some of its improvements ...
متن کاملOn Some Matrix Trace Inequalities
A is further called positive definite, symbolized A > 0, if the strict inequality in 1.1 holds for all nonzero x ∈ C. An equivalent condition forA ∈ Mn to be positive definite is thatA is Hermitian and all eigenvalues of A are positive real numbers. Given a positive semidefinite matrix A and p > 0, A denotes the unique positive semidefinite pth power of A. Let A and B be two Hermitian matrices ...
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: Malaya Journal of Matematik
سال: 2020
ISSN: 2319-3786,2321-5666
DOI: 10.26637/mjm0s20/0083