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Mathematics 2017, 5(4), 79; doi:10.3390/math5040079

Convertible Subspaces of Hessenberg-Type Matrices

1
Faculdade de Ciências, Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal
2
Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal
3
Center for Research and Development in Mathematics and Applications (CIDMA), Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
*
Author to whom correspondence should be addressed.
Received: 16 November 2017 / Revised: 9 December 2017 / Accepted: 10 December 2017 / Published: 13 December 2017
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Abstract

We describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. An explicit characterization of convertible Hessenberg-type matrices is presented. We conclude that convertible matrices with the maximum number of nonzero entries can be reduced to a basic set. View Full-Text
Keywords: determinant; permanent; Hessenberg matrix; convertible matrix determinant; permanent; Hessenberg matrix; convertible matrix
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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da Cruz, H.F.; Rodrigues, I.I.; Serôdio, R.; Simões, A.; Velhinho, J. Convertible Subspaces of Hessenberg-Type Matrices. Mathematics 2017, 5, 79.

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