矩阵值Carathéodory函数广义块Pick矩阵的秩不变性

摘要

Lasarow[1] derived statements on the rank invariance of generalized block Pick matrices of matrix-valued Caratheodory 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 [2]. These results are used to improve the proof of the rank invariance of the generalized block Pick matrices in certain sence.%Lasarow[1]推导出矩阵值Carathéodory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Carathéodory函数的值与它的直到某阶的导数值确定.利用文献[2]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.