On Integer Matrices Obeying Certain Matrix Equations
نویسنده
چکیده
We discuss integer matrices B of odd order v which satisfy Br = ± B, BBr = vI J, BJ = O. Matrices of this kind which have zero diagonal and other elements ± 1 give rise to skew-Hadamard and n-type matrices; we show that the existence of a skew-Hadamard (n-type) matrix of order h implies the existence of skew-Hadamard (n-type) matrices of orders (h 1)5 + 1 and (h 1)7 + 1. Finally we show that, although there are matrices B with elements other than ± 1 and 0, the equations force considerable restrictions on the elements of B. Disciplines Physical Sciences and Mathematics Publication Details Jennifer Seberry Wallis, On integer matrices obeying certain matrix equations, Journal of Combinatorial Theory, Ser. A., 12, (1972), 112-118. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/940 Reprinted from JOURNAL OF COMBINATORIAL THEORY All Rights Reserved by Academic Press, New York and London Vol. 12, No. I, January 1972 Printed in Belgium On Integer Matrices Obeying Certain Matrix Equations
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 12 شماره
صفحات -
تاریخ انتشار 1972