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Open AccessFeature PaperArticle

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.
Mathematics 2017, 5(4), 79; https://doi.org/10.3390/math5040079
Received: 16 November 2017 / Revised: 9 December 2017 / Accepted: 10 December 2017 / Published: 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
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. https://doi.org/10.3390/math5040079

AMA Style

Da Cruz HF, Rodrigues II, Serôdio R, Simões A, Velhinho J. Convertible Subspaces of Hessenberg-Type Matrices. Mathematics. 2017; 5(4):79. https://doi.org/10.3390/math5040079

Chicago/Turabian Style

Da Cruz, Henrique F.; Rodrigues, Ilda I.; Serôdio, Rogério; Simões, Alberto; Velhinho, José. 2017. "Convertible Subspaces of Hessenberg-Type Matrices" Mathematics 5, no. 4: 79. https://doi.org/10.3390/math5040079

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