Cq（D）上扩展型广义块Pick矩阵的秩不变性

摘要

In this paper, it is proved that the rank of extended generalized block Pick matrices of matrix-valued Caratheodory functions coincides with the rank of some block Toeplitz matrices by means of Toeplitz vector approach. Thus the rank invariance of extended generalized block Pick matrices is proved.%利用块Toeplitz向量方法，证明同一个矩阵值Caratheodory函数的扩展型广义块Pick矩阵的秩重合于具有秩不变性的块Toeplitz矩阵的秩，从而证明了该类型的广义块Pick矩阵的秩不变性．