On the Craig–Sakamoto theorem and Olkin’s determinantal result Original Research Article

Let A and B be any n×n real symmetric matrices. The following fact is well known: If In−αA−βB=In−αAIn−βB for any α, image, then AB=0. There exist various proofs. In this paper, we refine Olkin’s method [Linear Algebra Appl. 264 (1997) 217]. Furthermore, his determinantal result is generalized.