New results on Schur complements for Dashnic–Zusmanovich-type matrices and applications

Shiyun Wang; Shiyun Wang

doi:10.3934/math.2026981

AIMS Mathematics

2026, Volume 11, Issue 8: 24304-24330. doi: 10.3934/math.2026981

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Research article

New results on Schur complements for Dashnic–Zusmanovich-type matrices and applications

Shiyun Wang ^,

College of Science, Shenyang Aerospace University, Shenyang, Liaoning 110136, China

Received: 23 May 2026 Revised: 13 July 2026 Accepted: 29 July 2026 Published: 10 August 2026
MSC : 15A45, 15A48

The Schur complement has a wide range of applications. This paper establishes more general conditions under which the Schur complement of a Dashnic–Zusmanovich-type (DZT) matrix remains a DZT matrix. The proposed criteria cover many cases not previously addressed. We also characterize the cases in which the Schur complement is a strictly diagonally dominant matrix or a Dashnic–Zusmanovich (DZ) matrix. Numerical examples demonstrate that our results provide quite general criteria. As an application, we obtain an estimate for the determinant of DZT matrices and solve a large system of equations by a Schur-based method.
- Dashnic–Zusmanovich-type matrix,
- Schur complement,
- determinant
Citation: Shiyun Wang. New results on Schur complements for Dashnic–Zusmanovich-type matrices and applications[J]. AIMS Mathematics, 2026, 11(8): 24304-24330. doi: 10.3934/math.2026981

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Abstract

The Schur complement has a wide range of applications. This paper establishes more general conditions under which the Schur complement of a Dashnic–Zusmanovich-type (DZT) matrix remains a DZT matrix. The proposed criteria cover many cases not previously addressed. We also characterize the cases in which the Schur complement is a strictly diagonally dominant matrix or a Dashnic–Zusmanovich (DZ) matrix. Numerical examples demonstrate that our results provide quite general criteria. As an application, we obtain an estimate for the determinant of DZT matrices and solve a large system of equations by a Schur-based method.

References

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