Publications

• PUBLICATIONS IN MAGAZINES

  • Borobia, Alberto; Canogar, Roberto.A simplification of the C-realizability criterion for the Nonnegative Inverse Eigenvalue Problem for integers. 2024. arxiv.org/abs/2401.07857

  • Borobia, Alberto; Canogar, Roberto; De Terán, Fernando. On the consistency of the matrix equation XTAX = B when B is skew-symmetric: improving the previous characterization. Linear and Multilinear Algebra (online 2023), pp. 1 - 27. 2023.    doi.org/10.1080/03081087.2023.2211720  arxiv.org/abs/2209.02312

  • Borobia, Alberto; Canogar, Roberto; De Terán, Fernando. The equation X^TAX=B with B skew-symmetric: how much of a bilinear form is skew-symmetric?. Linear and Multilinear Algebra. 71 (2023), pp. 2114 - 2143.  doi.org/10.1080/03081087.2022.2093825  arxiv.org/abs/2203.07100

  • Borobia, Alberto; Canogar, Roberto; De Terán, Fernando. On the consistency of the matrix equation X^TAX=B when B is symmetric: the case where CFC(A) includes skew-symmetry blocks. Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas. 117 / 2 / 61 (2023), pp. 1 - 14.  doi.org/10.1007/s13398-023-01391-0  arxiv.org/abs/2209.02312

  • Borobia, Alberto; Canogar, Roberto. Nonsparse companion Hessenberg matrices. Electronic Journal of Linear Algebra. 37 (2021), pp. 193 - 210.  doi.org/10.13001/ela.2021.5405  arxiv.org/abs/2001.06470 

  • Borobia, Alberto; Canogar, Roberto; De Terán, Fernando. On the consistency of the matrix equation X^TAX=B when B is symmetric. Mediterranean Journal of Mathematics. 18 (2021), pp. 1 - 25.  doi.org/10.1007/s00009-020-01656-7

  • Borobia, Alberto; Canogar, Roberto. The WST-decomposition for partial matrices. Linear Algebra and its Applications. 564 (2019), pp. 95 - 125.  doi.org/10.1016/j.laa.2018.11.028  arxiv.org/abs/1805.10825

  • Borobia, Alberto. Fillmore's theorem for integer matrices. Linear Algebra Appl. 527 (2017), 281-284.  doi.org/10.1016/j.laa.2017.06.011  arxiv.org/abs/1704.08037

  • Borobia, Alberto; Canogar, Roberto. ACI-matrices of constant rank over arbitrary fields. Linear Algebra Appl. 527 (2017), 232-259.  doi.org/10.1016/j.laa.2017.04.002  arxiv.org/abs/1604.03447

  • Borobia, Alberto; Canogar, Roberto. The real nonnegative inverse eigenvalue problem is NP-hard. Linear Algebra Appl. 522 (2017), 127-139.  doi.org/10.1016/j.laa.2017.02.010  arxiv.org/abs/1608.00931

  • Borobia, Alberto; Canogar, Roberto. A note on matrices with prescribed off-diagonal submatrix and characteristic polynomial. Linear Algebra Appl. 458 (2014), 99-107.  doi.org/10.1016/j.laa.2014.06.005

  • Borobia, Alberto; Canogar, Roberto. Characterization of full rank ACI-matrices over fields. Linear Algebra Appl. 438 (2013), 3752-3762.  doi.org/10.1016/j.laa.2013.09.042

  • Borobia, Alberto; Canogar, Roberto. Nonsingular ACI-matrices over integral domains. Linear Algebra Appl. 436 (2012), 4311-4316.  doi.org/10.1016/j.laa.2011.12.038

  • Borobia, Alberto; Canogar, Roberto. Matrix completion problems over integral domains: The case with a diagonal of prescribed blocks. Linear Algebra Appl. 436 (2012), no. 1, 222–236.  doi.org/10.1016/j.laa.2011.06.049

  • Borobia, Alberto; Canogar, Roberto; Šmigoc, Helena. A matrix completion problem over integral domains: the case with 2n−3 prescribed entries. Linear Algebra Appl. 433 (2010), no. 3, 606–617.  doi.org/10.1016/j.laa.2010.03.025

  • Borobia, Alberto; Canogar, Roberto. A note on: "Constructing matrices with prescribed off-diagonal submatrix and invariant polynomials". Linear Algebra Appl. 429 (2008), no. 7, 1684–1686.  doi.org/10.1016/j.laa.2008.05.001

  • Borobia, Alberto; Moro, Julio; Soto, Ricardo. A unified view on compensation criteria in the real nonnegative inverse eigenvalue problem. Linear Algebra Appl. 428 (2008), no. 11-12, 2574–2584.  doi.org/10.1016/j.laa.2007.11.031

  • Borobia, Alberto. Inverse eigenvalue problems (Chapter 20). Handbook of linear algebra. Edited by Leslie Hogben. Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2007.  doi.org/10.1201/b16113

  • Borobia, Alberto; Canogar, Roberto. Constructing matrices with prescribed off-diagonal submatrix and invariant polynomials. Linear Algebra Appl. 424 (2007), no. 2-3, 615–633.  doi.org/10.1016/j.laa.2006.03.030

  • Soto, Ricardo; Rojo, Oscar; Moro, Julio; Borobia, Alberto. Symmetric nonnegative realization of spectra. Electron. J. Linear Algebra 16 (2007), 1–18.  doi.org/10.13001/1081-3810.1178

  • Borobia, Alberto. Constructing matrices with prescribed main-diagonal submatrix and characteristic polynomial. Linear Algebra Appl. 418 (2006), no. 2-3, 886–890.

  • Borobia, Alberto; Dormido, Sebastián. Three coefficients of a polynomial can determine its φ-instability. Linear Algebra Appl. 416 (2006), no. 2-3, 857–867.

  • Soto, Ricardo; Borobia, Alberto; Moro, Julio. On the comparison of some realizability criteria for the real nonnegative inverse eigenvalue problem. Linear Algebra Appl. 396 (2005), 223–241.

  • Borobia, Alberto; Moro, Julio; Soto, Ricardo. Negativity compensation in the nonnegative inverse eigenvalue problem. Linear Algebra Appl. 393 (2004), 73–89, 15A18

  • Borobia, Alberto; Dormido, Sebastián. Three coefficients of a polynomial can determine its instability. Linear Algebra Appl. 338 (2001), 67–76. (Reviewer: Vimal Singh), 93D09 (34D99)

  • Borobia, Alberto; Moro, Julio. On the boundary of the set of real spectra of nonnegative matrices. Linear Algebra Appl. 278 (1998), no. 1-3, 287–293. (Reviewer: Marc Artzrouni), 15A18 (15A48)

  • Kästner, Jochen; Borobia, Alberto; Dress, Andreas; Zylka, Christian. Extremal majorizing and anti-majorizing matrices. Linear Algebra Appl. 278 (1998), no. 1-3, 133–145. (Reviewer: Werner Kratz), 15A39 (15A90)

  • Borobia, Alberto; Chumillas, Valerio. ∗-graphs of vertices of the generalized transitive tournament polytope. Discrete Math. 179 (1998), no. 1-3, 49–57, 05C20

  • Borobia, Alberto; Cantó, Rafael. Matrix scaling: a geometric proof of Sinkhorn's theorem. Linear Algebra Appl. 268 (1998), 1–8.

  • Borobia, Alberto; Mazurovskiĭ, Vladimir. Nonsingular configurations of 7 lines of RP3. J. Knot Theory Ramifications 6 (1997), no. 6, 751–783.

  • Borobia, Alberto; Moro, Julio. On nonnegative matrices similar to positive matrices. Linear Algebra Appl. 266 (1997), 365–379.

  • Borobia, Alberto. Vertices of the generalized transitive tournament polytope. Discrete Math. 163 (1997), no. 1-3, 229–234.

  • Borobia, Alberto. A practical criterion for multivariate majorization. Rev. Acad. Canaria Cienc. 8 (1996), no. 1, 93–100.

  • Borobia, Alberto; Nutov, Zeev; Penn, Michal. Doubly stochastic matrices and dicycle covers and packings in Eulerian digraphs. Linear Algebra Appl. 246 (1996), 361–371.

  • Borobia, Alberto; Mazurovskiĭ, Vladimir. On diagrams of configurations of 7 skew lines of R3. Topology of real algebraic varieties and related topics, 33–40, Amer. Math. Soc. Transl. Ser. 2, 173, Amer. Math. Soc., Providence, RI, 1996.

  • Borobia, Alberto. On the nonnegative eigenvalue problem. Special issue honoring Miroslav Fiedler and Vlastimil Pták. Linear Algebra Appl. 223/224 (1995), 131–140.

  • Borobia, Alberto. (0,1/2,1) matrices which are extreme points of the generalized transitive tournament polytope. Proceedings of the Workshop "Nonnegative Matrices, Applications and Generalizations'' and the Eighth Haifa Matrix Theory Conference (Haifa, 1993). Linear Algebra Appl. 220 (1995), 97–110.

  • Borobia, Alberto. Mirror property for nonsingular mixed configurations of lines and points in R3. Discrete Comput. Geom. 11 (1994), no. 3, 311–320.

  • Borobia, Alberto. Diagonals of rotation matrices. Linear Algebra Appl. 186 (1993), 227–233.

  • Borobia, Alberto. Mirror property for nonsingular mixed configurations of one line and k points in R3. Real algebraic geometry (Rennes, 1991), 140–144, Lecture Notes in Math., 1524, Springer, Berlin, 1992.

  • Borobia, Alberto; Trías, Ujué. A geometric proof of the Perron-Frobenius theorem. Rev. Mat. Univ. Complut. Madrid 5 (1992), no. 1, 57–63.