Abstract

LetA be anM-matrix in standard lower block triangular form, with diagonal blocksAii irreducible. LetS be the set of indices α such that the diagonal blockAαα is singular. We define the singular graph ofA to be the setS with partial order defined by α > β if there exists a chain of non-zero blocksAαi, Aij, ⋯, Alβ.

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