Abstract A complex square matrix is called a ray nonsingular matrix (RNS matrix) if its ray pattern implies that it is nonsingular. A matrix M = I − A ( W ) is called a cycle tree matrix if the adjacency structure of the cycles in the arc-weighted digraph W (with no multi-arcs or loops), which is described by the cycle graph of W , is a tree. In this paper, it is shown that if there is no positive cycle in W , then the cycle tree matrix M = I − A ( W ) is a forbidden structure for RNS if and only if M is not RNS.

中文翻译：

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无正循环的循环树矩阵中射线非奇异性的禁止结构

摘要 如果一个复方矩阵的射线模式暗示它是非奇异的，则称为射线非奇异矩阵（RNS 矩阵）。矩阵 M = I − A ( W ) 被称为循环树矩阵，如果弧加权有向图 W 中循环的邻接结构（没有多弧或循环），由 W 的循环图描述，是一棵树。在本文中，表明如果 W 中不存在正循环，则当且仅当 M 不是 RNS 时，循环树矩阵 M = I − A ( W ) 是 RNS 的禁止结构。