Abstract

The paper presents new pseudoblock diagonal-dominance conditions for matrices with fixed block partitioning, which generalize the pointwise kth-order diagonal-dominance conditions and pointwise circuit diagonal-dominance conditions. For matrices satisfying pseudoblock conditions, the singularity/nonsingularity problem is considered. In particular, for block 2 × 2 matrices, certain known results are improved and generalized. Some eigenvalue inclusion regions corresponding to pseudoblock nonsingularity conditions are presented. Bibliography: 11 titles.

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