Concavity of monotone matrix functions of finite order
Concavity of monotone matrix functions of finite order
复制标题
有限阶单调矩阵函数的凹性
DOI：
10.1080/03081089008818003
复制
发表时间：
1990
影响因子：
1.1
通讯作者：
Roy Math Ias
中科院分区：
文献类型：
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作者：
Roy Math Ias
设f(0，∞)→R)是n阶单调矩阵函数，n的某一固定值.我们证明了f是[n/2]阶的矩阵凹函数，且对所有n×n正半定矩阵A和B，以及所有酉不变模都成立.因为f不是所有阶的单调矩阵函数，所以Loewner对所有阶单调的函数的积分表示不适用，相反，我们用f的泛函刻画来证明这些结果。
Let f (0, ∞) → R be a monotone matrix function of order n for some arbitrary but fixed value of n. We show that f is a matrix concave function of order [n/2] and that for all n-by-n positive semidefinite matrices A and B, and all unitarily invariant norms . Because f is not assumed to be a monotone matrix function of all orders, Loewner's integral representation of functions that are monotone of all orders is not applicable, instead we use the functional characterization of f in proving these results.