重庆理工大学学报:自然科学
重慶理工大學學報:自然科學
중경리공대학학보:자연과학
Journal of Chongqing Institute of Technology
2012年
12期
134-136,140
,共4页
Hermite矩阵%Hadamard乘积%迹不等式
Hermite矩陣%Hadamard乘積%跡不等式
Hermite구진%Hadamard승적%적불등식
Hermite matrices%Hadamard product%inequalities of trace.
研究了基于Hadamard乘积下矩阵迹的几个不等式,如Bellman型不等式、Young型不等式及其他几个不等式。得到主要结论:Bellman型不等式,设A,B∈Hn×n≥0,n为正整数,则tr(A。B)n=tr(An。Bn)≤trAn·trBn≤(trA)n·(trB)n;Young型不等式,设A,B∈Hn×n≥0,p〉1,q〉1,1/p+1/q=1,则tr (A。B)≤1/ptrAp+1/qtrBq。
研究瞭基于Hadamard乘積下矩陣跡的幾箇不等式,如Bellman型不等式、Young型不等式及其他幾箇不等式。得到主要結論:Bellman型不等式,設A,B∈Hn×n≥0,n為正整數,則tr(A。B)n=tr(An。Bn)≤trAn·trBn≤(trA)n·(trB)n;Young型不等式,設A,B∈Hn×n≥0,p〉1,q〉1,1/p+1/q=1,則tr (A。B)≤1/ptrAp+1/qtrBq。
연구료기우Hadamard승적하구진적적궤개불등식,여Bellman형불등식、Young형불등식급기타궤개불등식。득도주요결론:Bellman형불등식,설A,B∈Hn×n≥0,n위정정수,칙tr(A。B)n=tr(An。Bn)≤trAn·trBn≤(trA)n·(trB)n;Young형불등식,설A,B∈Hn×n≥0,p〉1,q〉1,1/p+1/q=1,칙tr (A。B)≤1/ptrAp+1/qtrBq。
In this paper,we get Bellman type,Young type and other inequalities based on the Hadamard product.The main conclusions are as follows: Bellman type inequality,Suppose A,B∈Hn×n≥0,n is positive integer,then tr(A。B)n=tr(An。Bn)≤trAn·trBn≤(trA)n·(trB)n;Young type inequality,Suppose A,B∈Hn×n≥0,p1,q1,1/p+1/q=1,then tr(A。B)≤1/ptrAp+1/qtrBq.