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Mathematics 2017, 5(4), 79;

Convertible Subspaces of Hessenberg-Type Matrices

Faculdade de Ciências, Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal
Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal
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
Full-Text   |   PDF [237 KB, uploaded 13 December 2017]


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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MDPI and ACS Style

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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