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On companion Boolean relation matrices. (English) Zbl 0882.05092

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.)
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