Chao, Chongyun; Wang, Tianming On companion Boolean relation matrices. (English) Zbl 0882.05092 J. Math. Res. Expo. 15, No. 2, 173-178 (1995). Summary: We prove a theorem concerning the powers of a companion matrix over the Boolean algebra \(B= (0,1)\) by using elementary properties of directed graphs. The main results in [Š. Schwarz, Czech. Math. J. 24(99), 252-253 (1974; Zbl 0315.15011)], [K. K. Butler and J. R. Krabill, Czech. Math. J. 24(99), 247-251 (1974; Zbl 0329.20049)] and [C. Chao and S. Winograd, Czech. Math. J. 27(102), 552-555 (1977; Zbl 0386.15014)] are consequences of our theorem. MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 15B33 Matrices over special rings (quaternions, finite fields, etc.) Keywords:Boolean relation matrices; companion matrix; directed graphs Citations:Zbl 0315.15011; Zbl 0329.20049; Zbl 0386.15014 PDFBibTeX XMLCite \textit{C. Chao} and \textit{T. Wang}, J. Math. Res. Expo. 15, No. 2, 173--178 (1995; Zbl 0882.05092)