On Rank Invariance of Generalized Block Pick Matrices of Matrix-valued Caratheodory Functions
矩阵值Caratheodory函数广义块Pick矩阵的秩不变性

Lasarow1] derived statements on the rank invariance of generalized block Pick matrices of matrix-valued Carath′eodory 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.