关于r-因子置换循环矩阵求逆与群逆的多项式快速算法

The Fast Polynomial Algorithm on Inverse and Group Inverse of Circulant Matrix of r-factor Permutation

提出r-因子置换循环矩阵概念,得到其相似标准形,从而得到该类矩阵可逆的多项式充要条件以及算法的理论依据。同时,得到的逆矩阵与群逆矩阵仍然是r-因子置换循环矩阵。最后,给出求逆矩阵和群逆矩阵的多项式快速算法及算例。

The concept of r-factor permutation circulant matrix was proposed and its similar canonical form was obtained,so as to the sufficient and necessary condition for invertible polynomial of such matrices and the theoretical basis of the algorithm were obtained.At the same time,the obtained inverse matrix and group inverse matrix was still the r-factor permutation circulant matrix.Finally,the procedure and example of polynomial fast algorithm for inverse matrix and group inverse matrix were given.