Chiru, I.E., Crivei, S. & Olteanu, G. (2023) Linear Algebra and its Applications [Domenii conexe, Q2]

Publicat: 09 Martie 2023

Chiru, I.E., Crivei, S. & Olteanu, G. (2023) Strongly regular matrices revisited. Linear Algebra and its Applications, 658, 233-249.

DOI: https://doi.org/10.1016/j.laa.2022.11.006

✓ Publisher: Elsevier
✓ Web of Science Categories: Mathematics, Applied; Mathematics
✓ Web of Science Article Influence Score (AIS): 0.643 (2023) / Q2 in all categories

Abstract: We prove a necessary condition and a sufficient condition for an n × n-matrix A with determinantal rank ρ(A) = t over an arbitrary commutative ring to be (von Neumann) strongly regular in terms of the trace of its tth compound
matrix Ct(A). In particular, a non-zero n × n-matrix A with ρ(A) = t over a local commutative ring R is strongly regular if and only if Tr(Ct(A)) is a unit in R, and in this case we construct a strong inner inverse of A. We derive applications to products of local commutative rings and group algebras. Finally, we count strongly regular matrices over some finite rings of residue classes and group algebras.

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