摘要
实数的几何平均概念也可推广到Hilbert空间上的自伴算子(矩阵),但其计算过程更复杂.通过矩阵的几何平均算法研究算子(矩阵)形式的Ky-Fan不等式,给出一个反例说明关于Hilbert空间上自伴算子(矩阵)的Ky-Fan不等式结果的猜想不成立.
The geometric mean concept about the real number can also be extended to the self-adjoint operators (matrices) in the Hilbert space,but the calculation process under such circumstances is more complicated.The Ky-Fan inequality of operator (matrix) is researched based on the algorithm of geometric mean about matrix.A counter example is provided to show that the result of speculation of KyFan inequality of self-adjoint operators (matrices) in the Hilbert space cannot be established.
出处
《东华大学学报(自然科学版)》
CAS
CSCD
北大核心
2014年第4期503-508,共6页
Journal of Donghua University(Natural Science)