A note on properties of splittings of singular symmetric positive semidefinite matrices (Q5944041)

\textit{M. Benzi} and \textit{D. B. Szyld} [Numer. Math. 76, 309-321 (1997; Zbl 0905.65048)] have investigated splitting of positive semidefinite matrices. A splitting \(A=B-C\) is called \(P\)-regular, if \(B+B^T-A\) is positive definite. A theorem on the \(P\)-regularity in that paper cannot be true. This is elucidated by an example in the paper under review.