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  Fernando C. Silva

Afiliação

Professor do Departamento de Matemática da Faculdade de Ciências da Universidade de Lisboa.
Membro do Centro de Análise Funcional, Estruturas Lineares e Aplicações.

Contactos

Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
fasilva@ciencias.ulisboa.pt
(+351) 217500290 (ext 26204)

Serviço Docente em 2016-17

Álgebra (mestrado em Matemática)
Álgebra Linear e Geometria Analítica
Álgebra III (licenciatura em Matemática)

Interesses científicos

Teoria das matrizes. Sistemas lineares e controlo. Álgebra.

Orientações de teses de doutoramento

  1. Susana Margarida Figueiredo de Sousa Borges Furtado, Problemas de Completação de Matrizes e Aplicações à Teoria do Controlo, Universidade de Lisboa, concluída em 24 de Janeiro de 2000.
  2. Enide Cascais Silva Andrade Martins, Invariantes de Semelhança de Comutadores de Matrizes, Universidade de Lisboa, concluída em 2 de Outubro de 2000.
  3. Glória Maria da Silva Pereira Cravo, Valores Próprios de Matrizes Parcialmente Conhecidas, Universidade de Lisboa, concluída em 9 de Janeiro de 2003.
  4. Laura Cristina Teixeira Iglésias, Alguns Problemas de Factorização de Matrizes, Universidade de Lisboa, concluída em 7 de Julho de 2006
  5. Marija Dodig, Completion of Matrices and Matrix Pencils. Problems of Control Theory, Universidade de Lisboa, concluída em 31 de Julho de 2006.
  6. Isabel Maria Teixeira de Matos, Problemas de Completação de Matrizes Reais, Universidade de Lisboa, concluída em 18 de Setembro de 2006.
  7. Rita Isabel Gonçalves Simões, Equação de Lyapunov e equação de Stein: Algumas Propriedades e Relações, Universidade de Lisboa, concluída em 20 de Março de 2009.
  8. Maria Cristina Canelas Lopes Ferreira, Sobre a Estabilização de Sistemas Lineares, Universidade de Lisboa, concluída em 24 de Abril de 2013.
  9. Maria da Graça Duffner Bessa Monteiro, Universidade de Lisboa, em curso.

Orientações de teses de mestrado

  1. Enide Cascais Silva Andrade Martins, Os Valores Próprios de $[X, A]$, Universidade de Lisboa, concluída em 4 de Novembro 1994.
  2. Helena Marilde Cardoso, Completação de uma Submatriz Arbitrária, Universidade de Lisboa, concluída em 30 de Maio 1997.
  3. Maria Cristina Canelas Lopes Ferreira, Estabilidade Matricial, Universidade de Lisboa, concluída em 17 de Janeiro 2000.
  4. Laura Cristina Teixeira Iglésias, Generalização de Fórmulas Min-Max e Teoremas de Entrelaçamento, Universidade de Lisboa, concluída em 28 de Fevereiro 2000.
  5. Rita Isabel Gonçalves Simões, Partição Característica Sujeita a Pequenas Perturbações, Universidade de Lisboa, concluída em 21 de Maio 2003.

Artigos de investigação

  1. On a conjecture about rational valued characters, Linear and Multilinear Algebra 15 (1984), 257-263.
  2. On the number of invariant polynomials of the matrix $XAX^{-1}+B$, Linear Algebra and Its Applications 79 (1986), 1-21.
  3. Matrices with prescribed eigenvalues and principal submatrices, Linear Algebra and Its Applications 92 (1987), 241-250.
  4. Matrices with prescribed characteristic polynomial and submatrices, Portugaliæ Mathematica 44 (1987), 261-264.
  5. On the invariant factors of the matrix $XAY+B$, Linear Algebra and Its Applications 96 (1987), 1-16.
  6. The eigenvalues of the sum of matrices with prescribed invariant polynomials, Linear and Multilinear Algebra 22 (1987), 7-13.
  7. Weakly polynomially complete pairs of matrices, Linear and Multilinear Algebra 22 (1987), 15-23.
  8. Spectrally complete pairs of matrices, Linear Algebra and Its Applications 108 (1988), 239-262.
  9. The eigenvalues of the sum of matrices with prescribed invariant polynomials II, Linear and Multilinear Algebra 24 (1988), 45-49.
  10. The rank of the difference of matrices with prescribed invariant factors, Linear and Multilinear Algebra 24 (1988), 59-63.
  11. The rank of the difference of matrices with prescribed similarity classes, Linear and Multilinear Algebra 24 (1988), 51-58.
  12. Matrices with prescribed similarity class and a prescribed nonprincipal submatrix, Portugaliæ Mathematica 47 (1990),103-113.
  13. Sums and products of matrices with prescribed similarity classes, Linear and Multilinear Algebra 27 (1990), 317-323.
  14. An additive inverse characteristic polynomial theorem, Portugaliæ Mathematica 47 (1990), 403-409.
  15. Matrices with nonzero entries, Linear Algebra and Its Applications 146 (1991), 111-119.
  16. Matrices with prescribed eigenvalues and blocks, Linear Algebra and Its Applications 148 (1991), 59-73.
  17. (Em colaboração com Isabel Cabral) Unified theorems on completions of matrix pencils, Linear Algebra and Its Applications 159 (1991), 43-54.
  18. (Em colaboração com Isabel Cabral) Similarity invariants of completions of submatrices, Linear Algebra and Its Applications 169 (1992), 151-161.
  19. Matrices with prescribed lower triangular part, Linear Algebra and Its Applications 182 (1993), 27-34.
  20. The eigenvalues of the product of matrices with prescribed similarity classes, Linear and Multilinear Algebra 34 (1993), 269-277.
  21. On the number of invariant polynomials of partially prescribed matrices, Linear Algebra and Its Applications 197/198 (1994), 709-754.
  22. (Em colaboração com Isabel Cabral) Controllability indices of partially prescribed pairs of matrices, Portugaliæ Mathematica 52 (1995), 175-192.
  23. (Em colaboração com Enide A. Martins) Eigenvalues of matrix commutators, Linear and Multilinear Algebra 39 (1995), 375-389.
  24. On controllability of partially prescribed matrices, Linear and Multilinear Algebra 40 (1995), 95-102.
  25. Integral representations of graphs, Portugaliæ Mathematica 53 (1996), 137-142.
  26. Possible block similarity classes of a matrix with a prescribed nonprincipal submatrix, Linear Algebra and Its Applications 249 (1996), 359-373.
  27. (Em colaboração com Wasin So) Possibilities for the number of invariant polynomials for the difference of two similarity classes, Linear and Multilinear Algebra 41 (1996), 289-302.
  28. (Em colaboração com M. Graça Marques) The characteristic polynomial of a matrix with prescribed off-diagonal blocks, Linear Algebra and Its Applications 250 (1997), 21-29.
  29. (Em colaboração com M. Graça Marques and Yu-Lin Zhang) The number of invariant polynomials of a matrix with prescribed complementary principal submatrices, Linear Algebra and Its Applications 251 (1997), 167-179.
  30. On a conjecture about the Jordan form of completions of partial upper triangular matrices, Linear Algebra and Its Applications 260 (1997), 319-321.
  31. (Em colaboração com Enide A. Martins) On the number of invariant polynomials of matrix commutators, Linear Algebra and Its Applications 262 (1997), 179-188.
  32. Possible block similarity classes of a matrix with a prescribed nonprincipal submatrix, II, Linear Algebra and Its Applications 262 (1997), 259-282.
  33. On feedback equivalence and completion problems, Linear Algebra and Its Applications 265 (1997), 231-245.
  34. (Em colaboração com Maria M. Torres) Rank partitions under small perturbations, Linear and Multilinear Algebra 43 (1997), 299-313.
  35. (Em colaboração com Catarina Santa-Clara) On infinite Goldie dimension, Journal of Algebra 205 (1998), 617-625.
  36. (Em colaboração com Susana Furtado) On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems, The Electronic Journal of Linear Algebra 4 (1998), 19-31.
  37. Invariant polynomials of matrices with prescribed entries, Linear and Multilinear Algebra 44 (1998), 357-372.
  38. (Em colaboração com Susana Furtado) On the characteristic polynomial of matrices with prescribed rows, Linear Algebra and Its Applications 293 (1999), 51-72.
  39. (Em colaboração com Orlando Neto) On the recognition and rigidity problems for sums of matrices, Linear Algebra and Its Applications 293 (1999), 73-84.
  40. (Em colaboração com Susana Furtado) Embedding a regular subpencil into a general linear pencil, Linear Algebra and Its Applications 295 (1999), 61-72.
  41. On the eigenvalues of matrices with prescribed upper triangular part, Linear and Multilinear Algebra 46 (1999), 117-138.
  42. (Em colaboração com Orlando Neto) Singular regular differential equations and eigenvalues of products of matrices, Linear and Multilinear Algebra 46 (1999), 145-164.
  43. On the number of invariant factors of partially prescribed matrices and control theory, Linear Algebra and Its Applications 311 (2000), 1-12.
  44. (Em colaboração com Glória Cravo) Eigenvalues of matrices with several prescribed blocks, Linear Algebra and Its Applications 311 (2000), 13-24.
  45. (Em colaboração com João Araújo) Semigroups of linear endomorphisms closed under conjugation, Communications in Algebra 28 (2000), 3679-3689.
  46. (Em colaboração com Isabel T. Matos) A completion problem over the field of real numbers, Linear Algebra and Its Applications 320 (2000), 63-77.
  47. (Em colaboração com Isabel Cabral and Ion Zaballa) Feedback invariants of pairs of matrices with prescribed columns, Linear Algebra and Its Applications 332-334 (2001), 447-458.
  48. (Em colaboração com Susana Furtado and Enide A. Martins) On similarity invariants of matrix commutators, Linear Algebra and Its Applications 335 (2001), 81-93.
  49. (Em colaboração com Glória Cravo and J. A. Dias da Silva) Characteristic polynomials and controlability of partially prescribed matrices, Linear Algebra and Its Applications 335 (2001), 157-166.
  50. (Em colaboração com Susana Furtado and Laura Iglésias) Products of matrices with prescribed spectra and ranks, Linear Algebra and Its Applications 340 (2002), 137-147.
  51. (Em colaboração com Susana Furtado and Laura Iglésias) Products of real matrices with prescribed characteristic polynomials, SIAM Journal on Matrix Analysis and Applications 23 (2002), 656-672.
  52. (Em colaboração com Enide A. Martins) On the eigenvalues of Jordan products, Linear Algebra and Its Applications 359 (2003), 249-262.
  53. (Em colaboração com Enide A. Martins) On the invariant polynomials of Jordan products, Linear Algebra and Its Applications 360 (2003), 173-189.
  54. (Em colaboração com Glória Cravo) Eigenvalues of matrices with several prescribed blocks II, Linear Algebra and Its Applications 364 (2003), 81-89.
  55. (Em colaboração com Glória Cravo) The number of nonconstant invariant polynomials of matrices with several prescribed blocks, Linear Algebra and Its Applications 368 (2003), 107-116.
  56. (Em colaboração com Jaspal Singh Aujla) Weak majorization inequalities and convex functions, Linear Algebra and Its Applications 369 (2003), 217-233.
  57. (Em colaboração com Cristina Ferreira) Inertia theorems for pairs of matrices, Linear Algebra and Its Applications 381 (2004), 37-52.
  58. (Em colaboração com Cristina Ferreira) On the stabilization of linear discrete-time systems, Linear Algebra and Its Applications 390 (2004), 7-18.
  59. (Em colaboração com Susana Furtado and Enide A. Martins) On similarity invariants of matrix commutators and Jordan products, Linear Algebra and Its Applications 401 (2005), 453-466.
  60. (Em colaboração com João Araújo) Semigroups of matrices closed under conjugation by normal linear groups, JP Journal of Algebra, Number Theory and Applications 5 (2005), 535-545.
  61. (Em colaboração com Cristina Ferreira) Inertia theorems for pairs of matrices, II, Linear Algebra and Its Applications 413 (2006), 425-439.
  62. (Em colaboração com Susana Furtado and Laura Iglésias), Eigenvalues of products of matrices, Linear and Multilinear Algebra, 54 (2006), 343-353.
  63. (Em colaboração com Rita Simões) On the Lyapunov and Stein equations, Linear Algebra and Its Applications 420 (2007), 329-338.
  64. (Em colaboração com Rita Simões) On the Lyapunov and Stein equations, II, Linear Algebra and Its Applications 426 (2007), 305-311.
  65. (Em colaboração com Marija Dodig) Controllability of series connections of arbitrarily many linear systems, Linear Algebra and Its Applications 429 (2008), 122-141.
  66. (Em colaboração com Isabel T. Matos) Completion problems for real matrices, II, Linear Algebra and Its Applications 432 (2010), 180–202.
  67. (Em colaboração com Laura Iglésias and Catarina Santa-Clara) Unified min-max and interlacing theorems for linear operators, Linear and Multilinear Algebra 59 (2011), 651-669.
  68. (Em colaboração com Rita Simões) Row and column rank partitions under small perturbations, Linear and Multilinear Algebra 60 (2012), 1-9.
  69. (Em colaboração com Alicia Roca) Pencils with prescribed constant subpencils, Linear Algebra and Its Applications 436 (2012), 3315–3336.
  70. (Em colaboração com Alicia Roca) Pencils with prescribed constant subpencils over arbitrary fields, Linear Algebra and Its Applications 445 (2014), 138–161.
  71. (Em colaboração com Maria da Graça Duffner) On the interlacing inequalities for invariant factors, Linear Algebra and Its Applications 486 (2015), 443-448.
  72. (Em colaboração com Laura Iglésias) Spectral and weak polynomial completeness for the product of nonsingular matrices, Linear and Multilinear Algebra 63 (2015), 1937-1946.
  73. (Em colaboração com Laura Iglésias) Weakly spectrally complete pair of matrices, Linear and Multilinear Algebra 64 (2016), 942-950.
  74. (Em colaboração com Maria da Graça Duffner) On the existence of unimodular matrices with a prescribed submatrix, Linear Algebra and Its Applications 515 (2017), 321-330.