Subdirect sums of weakly chained diagonally dominant matrices

Abstract

Some sufficient conditions ensuring that the subdirect sum of two weakly chained diagonally dominant matrices is in this class, are given. In particular, it is shown that the subdirect sum of overlapping principal submatrices of a weakly chained diagonally dominant matrix is also a weakly chained diagonally dominant matrix.

Keywords:

• Subdirect sum
• weakly chained diagonally dominant matrices
• irreducible diagonally dominant matrices

AMS Subject Classifications:

• 15A06
• 15A42
• 15A48

Acknowledgements

The authors are grateful to the referees and the editor Prof. Bojan Kuzma for their useful and constructive suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundations of China [grant number 11361074], [grant number 11601473]; CAS ‘Light of West China’ Program.