AI 中文总结
本文利用非循环或树对角矩阵逆的刻画，构造逆为非循环Z-矩阵的矩阵，并建立多类矩阵间的关系。
AI 中文摘要
Kle在其里程碑式论文中对非循环或树对角矩阵的逆给出了良好刻画，Nab01也给出了与三对角矩阵逆结构相关的这类逆的刻画。本文利用该刻画确定并构造逆为非循环Z-矩阵的矩阵，还建立了Z-矩阵、逆Z-矩阵、超度量矩阵、广义超度量矩阵、移位超度量矩阵、非循环矩阵、逆非循环矩阵、树结构矩阵、cyclopes及广义cyclopes等几类矩阵之间的关系。
英文摘要
Inverses of acyclic or treediagonal matrices are nicely characterized in the landmarked paper by Klein \cite{KLe82}. But also in \cite{Nab01} a characterization of these inverses is given which is related to the structure of inverses of tridiagonal matrices. Here we use this characterization to determine and construct matrices whose inverses are acyclic $Z$-matrices. Moreover, we establish relations between several classes of matrices, namely the classes of $Z$-matrices, inverse $Z$-matrices, ultrametric matrices, generalized ultrametric matrices, shifted ultrametric matrices, acyclic matrices, inverse acyclic matrices, matrices of tree structure, cyclopes and generalized cyclopes.
Comments21 pages
