一类广义Vandermonde矩阵的求逆问题

The Inverse Problem of Generalized Vandermonde Matrix

Vandermonde矩阵是矩阵理论中一个重要的矩阵类型,它的许多广义形式在处理矩阵问题时能起到关键的作用.当子块Di的阶数li比较大时,利用分块矩阵法给出了一类广义Vandermonde矩阵D的求逆方法及其逆矩阵的分块结构表达式.

The Vandermonde matrix is an important type of matrix in matrix theory, and many of its gen-eralized forms are playing a key role in processing matrix problems. This paper provides the method of inverse of generalized Vandermonde matrix D and the block structure expression of its inversed matrix by using block matrices when the order number li of block matrix Di is comparatively large.