اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدInequalities regarding partial trace and partial determinant
75
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we first present simple proofs of Chois results [4], then we give a short alternative proof for Fiedler and Markhams inequality [6]. We also obtain additional matrix inequalities related to partial determinants.
قيم البحث
اقرأ أيضاً
A formula for the partial trace of a full symmetrizer is obtained. The formula is used to provide an inductive proof of the well-known formula for the dimension of a full symmetry class of tensors.
The trace regression model, a direct extension of the well-studied linear regression model, allows one to map matrices to real-valued outputs. We here introduce an even more general model, namely the partial-trace regression model, a family of linear
mappings from matrix-valued inputs to matrix-valued outputs; this model subsumes the trace regression model and thus the linear regression model. Borrowing tools from quantum information theory, where partial trace operators have been extensively studied, we propose a framework for learning partial trace regression models from data by taking advantage of the so-called low-rank Kraus representation of completely positive maps. We show the relevance of our framework with synthetic and real-world experiments conducted for both i) matrix-to-matrix regression and ii) positive semidefinite matrix completion, two tasks which can be formulated as partial trace regression problems.
We show that ||u*u - v*v|| leq ||u - v|| for partial isometries u and v. There is a stronger inequality if both u and v are extreme points of the unit ball of a C*-algebra, and both inequalities are sharp. If u and v are partial isometries in a C*-al
gebra A such that ||u - v|| < 1, then u and v are homotopic through partial isometries in A. If both u and v are extremal, then it is sufficient that ||u - v|| < 2. The constants 1 and 2 are both sharp. We also discuss the continuity points of the map which assigns to each closed range element of A the partial isometry in its canonical polar decomposition.
Let $A$ be a positive semidefinite $mtimes m$ block matrix with each block $n$-square, then the following determinantal inequality for partial traces holds [ (mathrm{tr} A)^{mn} - det(mathrm{tr}_2 A)^n ge bigl| det A - det(mathrm{tr}_1 A)^m bigr|, ]
where $mathrm{tr}_1$ and $mathrm{tr}_2$ stand for the first and second partial trace, respectively. This result improves a recent result of Lin [14].
Let $A$ be an $mtimes m$ positive semidefinite block matrix with each block being $n$-square. We write $mathrm{tr}_1$ and $mathrm{tr}_2$ for the first and second partial trace, respectively. In this note, we prove the following inequality [ (mathrm{t
r} A)I_{mn} - (mathrm{tr}_2 A) otimes I_n ge pm bigl( I_motimes (mathrm{tr}_1 A) -Abigr). ] This inequality is not only a generalization of Andos result [1], but it also could be regarded as a complement of a recent result of Choi [8]. Additionally, some new partial traces inequalities for positive semidefinite block matrices are also included.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
