Criteria And Inclusion Regions Of Eigenvalues Of Block α-Diagonally Dominant Matrices

Diagonally dominant matrices play an important role in numerical mathematics , economics and statistics .Many scholars have given important conclusions on them.In this paper, several sufficient and necessary conditions of blockα-diagonally dominant matrices and the sufficient conditions of block H-matrices are given, which generalize the theory ofα-diagonally dominant matrices to blockα-diagonally dominant matrices. And we give the new criteria for numerical and relevant fields. As an application , the inclusion region of eigenvalues of blockα-diagonally dominant matrices are given.