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Canogar Mckenzie, Roberto

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0000-0002-6952-9311
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Canogar Mckenzie
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Roberto
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2015 - 201912020 - 20233
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Nivel de acceso: info:eu-repo/semantics/openAccess × Autor: Canogar Mckenzie, Roberto ×

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Mostrando 1 - 4 de 4
  • Miniatura
    Publicación
    On the consistency of the matrix equation X^TAX=B when B is symmetric: the case where CFC(A) include skew-symmetric blocks
    (Springer, 2022-03-17) Borobia Vizmanos, Alberto; De Terán, Fernando; Canogar Mckenzie, Roberto
    In this paper, which is a follow-up to [A. Borobia, R. Canogar, F. De Ter´an, Mediterr. J. Math. 18, 40 (2021)], we provide a necessary and sufficient condition for the matrix equation XJAX “ B to be consistent when B is symmetric. The condition depends on the canonical form for congruence of the matrix A, and is proved to be necessary for all matrices A, and sufficient for most of them. This result improves the main one in the previous paper, since the condition is stronger than the one in that reference, and the sufficiency is guaranteed for a larger set of matrices (namely, those whose canonical form for congruence, CFC(A), includes skew-symmetric blocks).
  • Miniatura
    Publicación
    Una demostración geométrica del teorema de Perron-Frobenius
    (Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2015-10-19) Baena Marzo, Gema María; Canogar Mckenzie, Roberto
    En este documento se pretende desarrollar con el máximo detalle y el máximo rigor matemático la demostración geométrica del Teorema de Perron-Frobenius publicada por los matemáticos D.Alberto Borobia y D. Ujué R. Trías, en el año 1992, en la Revista Matemática de Universidad Complutense de Madrid (Vol.5, nº 1).
  • 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.
  • 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.