2023/08/08 by Khurana, Dinesh, Lam, T. Y.
#15A15 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2308.04411
For any three n× n matrices A,B,X over a commutative ring S, we prove that \rm det (A+B-AXB)=\rm det (A+B-BXA) ∈ S. This apparently new formula may be regarded as a ``ternary generalization'' of Sylvester's classical determinantal formula \rm det (In-AB)=\rm det (In-BA) for any pair of n× n matrices A,B over S.