矩阵值Caratheodory函数广义块Pick矩阵的秩不变性  

On Rank Invariance of Generalized Block Pick Matrices of Matrix-valued Caratheodory Functions

作　　者：贺勤[1] 徐清舟[2] 陈公宁[1,3] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]许昌学院国际教育学院,河南许昌461000 [3]北京师范大学数学科学学院,北京100875

出　　处：《数学物理学报（A辑）》2012年第1期103-112,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(10701009)资助

摘　　要：Lasarow推导出矩阵值Caratheodory函数的第一、第二型广义块Pick矩阵及其变型的秩不变性.这些矩阵由同一个Caratheodory函数的值与它的直到某阶的导数值确定.利用文献中提出的块Toeplitz向量方法,该文断言,这些块矩阵的秩分别相关并重合于具有秩不变性的块Toeplitz矩阵的秩,从而改进了这两类广义块Pick矩阵的秩不变性结论的证明.Lasarow derived statements on the rank invariance of generalized block Pick matrices of matrix-valued Carath@odory functions. In this paper, it is concluded that the rank of such generalized block Pick matrices can be related to and coincides with the rank of some block Toeplitz matrices in terms of the Toeplitz vector approach given in . These results are used to improve the proof of the rank invariance of the generalized block Pick matrices in certain sence.

关 键 词：q×q CARATHEODORY函数 广义块Pick矩阵 块Toeplitz矩阵 秩不变性. 

分 类 号：O241.3[理学—计算数学]