当前位置: X-MOL 学术Linear Multilinear Algebra › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the matrix Heron means and Rényi divergences
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-05-13 , DOI: 10.1080/03081087.2020.1763239
Trung Hoa Dinh 1 , Raluca Dumitru 2 , Jose A. Franco 2
Affiliation  

Bhatia, Lim, and Yamazaki studied the norm minimality of several Kubo-Ando means of positive semidefinite matrices. Recently, Hiai proved a norm minimality result involving the the weighted geometric mean A1αB=A1/2(A1/2BA1/2)1αA1/2, 0α1 and its ‘naïve’ extension given by Qα,z(A,B)=(B1α2zAαzB1α2z)z, which is a matrix function in the definition of the quantum α-z-Rényi divergence. In connection to these results, for positive semidefinite matrices, we show that the inequality A+B+2rA1αBpA+B+2rQα,z(A,B)p, holds for p = 1, 2, α=1,z, and r0, among other related inequalities.



中文翻译:

关于矩阵 Heron 均值和 Rényi 散度

Bhatia、Lim 和 Yamazaki 研究了正半定矩阵的几个 Kubo-Ando 均值的范数极小性。最近,Hiai 证明了一个涉及加权几何平均值的范数极小结果一种1-α=一种1/2(一种-1/2一种-1/2)1-α一种1/2, 0α1及其“天真的”扩展由α,z(一种,)=(1-α2z一种αz1-α2z)z,它是量子α - z -Rényi散度定义中的矩阵函数。结合这些结果,对于半正定矩阵,我们证明了不等式一种++2r一种1-αp一种++2rα,z(一种,)p,p =  1, 2,α=1,z, 和r0,以及其他相关的不平等。

更新日期:2020-05-13
down
wechat
bug