Abstract
LetF be a field,v(≥2) an integer,I v the identity matrix of orderv, andJ v the all-one matrix of orderv. LetD={αI v+βJ v∈GL v(F)|α,β∈F}, and ℊ={C∈GL v(F)| the row-sums and the column-sums ofC are all equal}. In this paper, we study (1) the center and the centralizer of ℊ, (2) the centralizer and the normalizer ofD whenv=2, and (3) the orders ofD, ℊ and the normalizer ofD.
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References
M. Hall, Jr., Combinatorial Theory, Blaisdell Publishing Company, 1967.
Wan Zhexian, Dai Zongduo, Feng Xuning and Yang Benfu, Studies in Finite Geometries and the Construction of Incomplete Block Designs, Science Press, Beijing, 1966.
Wei Wandi, The Properties of MatricesαI+βJ and Their Applications,Nature Journal,6: 10 (1987), 473.
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Wei, W., Yang, B. The properties of matricesαI+βJ and some related problems. Acta Mathematicae Applicatae Sinica 4, 333–339 (1988). https://doi.org/10.1007/BF02007237
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DOI: https://doi.org/10.1007/BF02007237