Convertible Subspaces of Hessenberg-Type Matrices

Henrique F. Da Cruz, Ilda Inácio Rodrigues, Rogério Serôdio, Alberto Simões and José Velhinho
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Henrique F. Da Cruz: Faculdade de Ciências, Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal
Ilda Inácio Rodrigues: Faculdade de Ciências, Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal
Rogério Serôdio: Faculdade de Ciências, Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal
Alberto Simões: Faculdade de Ciências, Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal
José Velhinho: Faculdade de Ciências, Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal

Mathematics, 2017, vol. 5, issue 4, 1-12

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.

Keywords: determinant; permanent; Hessenberg matrix; convertible matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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