一类对称Loewner矩阵及其可逆性

A Kind of Symmetric Loewner Matrices and Their Invertibility

利用对称Loewner矩阵与有理函数插值之间的内在联系,给出一类对称Loewner矩阵非奇异的充要条件,并给出逆矩阵的明确表达式,以及满足一定条件的奇异对称Loewner矩阵的Moore-Penrose逆的明确表达式。

On the basis of intrinsic connections between symmetric Loewner matrix and interpolation for rational functions, this paper gives necessary and sufficient conditions for the invertibility of a complex symmetric Loewner matrix. An explicit formula for the inverse is given when these conditions are met. An explicit formula for Moore-Penrose generalized inverse of a singular symmetric Loewner matrix under certain conditions is also presented.