Fernando C. Silva

Professor at the Math Department of the Faculty of Science of the University of Lisbon

Member of the Center for Linear Structures and Combinatorics

Mail: Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal

Phone: (351) 21 750 02 90 (Ext.: 26204)

Fax: (351) 21 750 00 72

E-mail: fasilva@fc.ul.pt

Research interests: Matrix Analysis. Linear Systems and Control. Algebra

Research Papers

  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. (With Isabel Cabral) Unified theorems on completions of matrix pencils, Linear Algebra and Its Applications 159 (1991), 43-54.
  18. (With 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. (With Isabel Cabral) Controllability indices of partially prescribed pairs of matrices, Portugaliæ Mathematica 52 (1995), 175-192.
  23. (With 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. (With 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. (With M. Graça Marques) The characteristic polynomial of a matrix with prescribed off-diagonal blocks, Linear Algebra and Its Applications 250 (1997), 21-29.
  29. (With 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. (With 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. (With Maria M. Torres) Rank partitions under small perturbations, Linear and Multilinear Algebra 43 (1997), 299-313.
  35. (With Catarina Santa-Clara) On infinite Goldie dimension, Journal of Algebra 205 (1998), 617-625.
  36. (With 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. (With Susana Furtado) On the characteristic polynomial of matrices with prescribed rows, Linear Algebra and Its Applications 293 (1999), 51-72.
  39. (With Orlando Neto) On the recognition and rigidity problems for sums of matrices, Linear Algebra and Its Applications 293 (1999), 73-84.
  40. (With 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. (With 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. (With Glória Cravo) Eigenvalues of matrices with several prescribed blocks, Linear Algebra and Its Applications 311 (2000), 13-24.
  45. (With João Araújo) Semigroups of linear endomorphisms closed under conjugation, Communications in Algebra 28 (2000), 3679-3689.
  46. (With Isabel T. Matos) A completion problem over the field of real numbers, Linear Algebra and Its Applications 320 (2000), 63-77.
  47. (With 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. (With Susana Furtado and Enide A. Martins) On similarity invariants of matrix commutators, Linear Algebra and Its Applications 335 (2001), 81-93.
  49. (With 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. (With Susana Furtado and Laura Iglésias) Products of matrices with prescribed spectra and ranks, Linear Algebra and Its Applications 340 (2002), 137-147.
  51. (With 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. (With Enide A. Martins) On the eigenvalues of Jordan products, Linear Algebra and Its Applications 359 (2003), 249-262.
  53. (With Enide A. Martins) On the invariant polynomials of Jordan products, Linear Algebra and Its Applications 360 (2003), 173-189.
  54. (With Glória Cravo) Eigenvalues of matrices with several prescribed blocks II, Linear Algebra and Its Applications 364 (2003), 81-89.
  55. (With Glória Cravo) The number of nonconstant invariant polynomials of matrices with several prescribed blocks, Linear Algebra and Its Applications 368 (2003), 107-116.
  56. (With Jaspal Singh Aujla) Weak majorization inequalities and convex functions, Linear Algebra and Its Applications 369 (2003), 217-233.
  57. (With Cristina Ferreira) Inertia theorems for pairs of matrices, Linear Algebra and Its Applications 381 (2004), 37-52.
  58. (With Cristina Ferreira) On the stabilization of linear discrete-time systems, Linear Algebra and Its Applications 390 (2004), 7-18.
  59. (With 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. (With 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. (With Cristina Ferreira) Inertia theorems for pairs of matrices, II, Linear Algebra and Its Applications 413 (2006), 425-439.
  62. (With Susana Furtado and Laura Iglésias), Eigenvalues of products of matrices, Linear and Multilinear Algebra, 54 (2006), 343-353.
  63. (With Rita Simões) On the Lyapunov and Stein equations, Linear Algebra and Its Applications 420 (2007), 329-338.
  64. (With Rita Simões) On the Lyapunov and Stein equations, II, Linear Algebra and Its Applications 426 (2007), 305-311.
  65. (With Marija Dodig) Controllability of series connections of arbitrarily many linear systems, Linear Algebra and Its Applications 429 (2008), 122-141.
  66. (With Isabel T. Matos) Completion problems for real matrices, II, Linear Algebra and Its Applications 432 (2010), 180–202.