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Borobia Vizmanos, Alberto

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0000-0001-7034-2426
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Borobia Vizmanos
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Alberto
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2017 - 201912020 - 20232
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Mostrando 1 - 3 de 3
  • Miniatura
    Publicación
    Congresos, seminarios, reuniones científicas y cursos de verano: IV Jornadas ALAMA: problemas espectrales inversos
    (Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2017-01-01) Borobia Vizmanos, Alberto
  • Miniatura
    Publicación
    Nonsparse Companion Hessenberg Matrices
    (International Linear Algebra Society (ILAS), 2021-03-05) Borobia Vizmanos, Alberto; Canogar Mckenzie, Roberto; Ministerio de Ciencia, Innovación y Universidades. España
    In recent years, there has been a growing interest in companion matrices. Sparse companion matrices are well known: every sparse companion matrix is equivalent to a Hessenberg matrix of a particular simple type. Recently, Deaett et al. [Electron. J. Linear Algebra, 35:223247, 2019] started the systematic study of nonsparse companion matrices. They proved that every nonsparse companion matrix is nonderogatory, although not necessarily equivalent to a Hessenberg matrix. In this paper, the nonsparse companion matrices which are unit Hessenberg are described. In a companion matrix, the variables are the coordinates of the characteristic polynomial with respect to the monomial basis. A PB-companion matrix is a generalization, in the sense that the variables are the coordinates of the characteristic polynomial with respect to a general polynomial basis. The literature provides examples with Newton basis, Chebyshev basis, and other general orthogonal bases. Here, the PB-companion matrices which are unit Hessenberg are also described.
  • Miniatura
    Publicación
    On the consistency of the matrix equation XTAX B when B is skew-symmetric: improving the previous characterization
    (Taylor and Francis Group, 2023-05-16) Borobia Vizmanos, Alberto; Canogar Mckenzie, Roberto; Teran, Fernando De; Ministerio de Ciencia e Innovación de España
    We provide a necessary and su cient condition for the matrix equation XTAX B to be consistent, when A is an arbitrary complex square matrix and B is skew-symmetric. This problem is equivalent to nd the largest dimension of a subspace in which the bilinear form A is symplectic. The necessity is valid for any A and B as above, whereas the su ciency is proved to be valid for any skew-symmetric matrix B and for all complex square matrices A whose Canonical form for congruence (CFC) does not contain blocks 0 1 1 1 . The provided condition improves the one in [A. Borobia, R. Canogar, F. De Teran, Lin. Multilin. Algebra, 2022. doi:10.1080/03081087.2022.2093825], because it includes the case where CFC(A) includes symmetric blocks, and it is given in terms of the size of A and the rank of its symmetric and skew-symmetric parts. More precisely, if A is n n, we prove that the equation is consistent if and only if rankB mintn nA rankpA ATq 2 NulAXNulAT.