First, some properties of parameters r, q, δ which satisfy these restricted equation by using the property of matrix trace were got.
从两方面探讨了Ｌｙａｐｕｎｏｖ方程的性质：即从矩阵迹的角度给出该方程成立的条件和从矩阵特征值的角度进一步讨论了相应的性
This paper has testified the matrix trace inequalities are more closely to arithmetical-geometrical average inequalities according to the inequality form, which brought forward as “matrix trace inequalities analogy to the arithmetical-geometrical average inequalities” by R.
Bellman提出的“类似于算术 -几何平均不等式的矩阵迹不等式”在形式上更接近算术-几何平均不等式的矩阵迹不等式 ｜tr( mk =1Ak) ｜1 /m ≤ 1m mk =1trAk 且证明了更一般的结论及相关重要结果｜tr( mk=1Atkk)｜1 /Tm ≤ 1Tm mk=1tk·tr(AkA k) 1 / 2 和｜ ti=1tr( mk=1A(i)k )｜≤ mk=1{ ti=1[tr(A(i)k A(i) k ) αk/ 2 ]βi/αk} 1 / βi,其中Tm = mk =1tk,tk,αk,βi 是正整数 , mk =1α-1k ≥ 1 , ti=1β-1i ≥ 1 。
In general,the trace of matrix deals only with square matrixs,and in this paper,we generalize this trace of matrix to general matrixs.
一般情况下,矩阵迹的计算只涉及到方阵。
Some inequalities of matrix-traces on C~*-algebra M_n(A);
关于C~*-代数M_n(A)上矩阵迹的一些不等式
In this note,for a C*-algebra A,we study the properties of a matrix-trace on the C*-algebra Mn(A) which is a positive linear mapping τ:Mn(A)→A,such that τ(u*au)=τ(a)(a∈Mn(A)),u∈U(Mn(A)) and τ(a2)≤(τ(a))2(a≥0),and obtain some inequalities on arithmetic-geometric mean.
对于C*-代数A,C*-代数Mn(A)上矩阵迹是一个正线性映射τ:Mn(A)→A,满足τ(u*au)=(τa)(a∈Mn(A)),u∈U(Mn(A))和τ(a2)≤(τ(a))2(a≥0)。
Bellman inequalities of generalized matrix trace;
广义矩阵迹的贝尔曼不等式(英文)