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

## Abstract

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 a_{1}...a_{n} which are non-negative integers that form either a non-decreasing or a symmetric unimodal sequence; then A_{k}=P_{k}(A) is a non-negative matrix, where p_{k} denotes the characteristic polynomial of the top k×k principal submatrix of A, for k=1,...,n. The matrices A_{k} as well as the eigenvalues of A, are explicitly described in some special cases, such as (i) a_{i}=0 for all ior (ii) a_{i}=0 for i < n and a_{n}=1. Characters ot finite abelian hypergroups are defined, and that naturally leads to harmonic analysis on such hypergroups.

Item Type: | Article |
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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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