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An identity between the determinant and the permanent of Hessenberg-type matrices

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Abstract

In this short note we provide an extension of the notion of Hessenberg matrix and observe an identity between the determinant and the permanent of such matrices. The celebrated identity due to Gibson involving Hessenberg matrices is consequently generalized.

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Authors and Affiliations

  1. Department of Mathematics, University of Coimbra, 3001-454, Coimbra, Portugal

    Carlos Martins da Fonseca

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  1. Carlos Martins da Fonseca
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Correspondence to Carlos Martins da Fonseca.

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This note is supported by CMUC — Centro de Matemática da Universidade de Coimbra.

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da Fonseca, C.M. An identity between the determinant and the permanent of Hessenberg-type matrices. Czech Math J 61, 917–921 (2011). https://doi.org/10.1007/s10587-011-0059-1

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