Czechoslovak Mathematical Journal, Vol. 61, No. 4, pp. 917-921, 2011

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

Carlos Martins da Fonseca

C. M. da Fonseca, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal, e-mail: cmf@mat.uc.pt

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.

Keywords: determinant, permanent, Hessenberg matrices, graphs, trees

Classification (MSC 2010): 15A15


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