On hypergroups of matrices

Bapat, R. B. ; Sunder, V. S. (1991) On hypergroups of matrices Linear and Multilinear Algebra, 29 (2). pp. 125-140. ISSN 0308-1087

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/0308108...

Related URL: http://dx.doi.org/10.1080/03081089108818063


After recalling the definition and some basic properties of finite hypergroups-a notion introduced in a recent paper by one of the authors-several non-trivial examples of such hypergroups are constructed. The examples typically consist of n n×n matrices, each of which is an appropriate polynomial in a certain tri-diagonal matrix. The crucial result required in the construction is the following: 'let A be the matrix with ones on the super-and sub-diagonals, and with main diagonal given by a1...an which are non-negative integers that form either a non-decreasing or a symmetric unimodal sequence; then Ak=Pk(A) is a non-negative matrix, where pk denotes the characteristic polynomial of the top k×k principal submatrix of A, for k=1,...,n. The matrices Ak as well as the eigenvalues of A, are explicitly described in some special cases, such as (i) ai=0 for all ior (ii) ai=0 for i < n and an=1. Characters ot finite abelian hypergroups are defined, and that naturally leads to harmonic analysis on such hypergroups.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Group.
ID Code:53553
Deposited On:09 Aug 2011 11:50
Last Modified:12 Jul 2012 06:32

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