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 2022-23
Álgebra I Álgebra II Teoria dos Códigos
Interesses científicos
Teoria das matrizes. Sistemas lineares e controlo. Álgebra.
Orientações de teses de doutoramento
- 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.
- Enide Cascais Silva Andrade Martins, Invariantes de Semelhança de Comutadores de Matrizes, Universidade de Lisboa, concluída em 2 de Outubro de 2000.
- Glória Maria da Silva Pereira Cravo, Valores Próprios de Matrizes Parcialmente Conhecidas, Universidade de Lisboa, concluída em 9 de Janeiro de 2003.
- Laura Cristina Teixeira Iglésias, Alguns Problemas de Factorização de Matrizes, Universidade de Lisboa, concluída em 7 de Julho de 2006
- Marija Dodig, Completion of Matrices and Matrix Pencils. Problems of Control Theory, Universidade de Lisboa, concluída em 31 de Julho de 2006.
- Isabel Maria Teixeira de Matos, Problemas de Completação de Matrizes Reais, Universidade de Lisboa, concluída em 18 de Setembro de 2006.
- 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.
- Maria Cristina Canelas Lopes Ferreira, Sobre a Estabilização de Sistemas Lineares, Universidade de Lisboa, concluída em 24 de Abril de 2013.
- Maria da Graça Duffner Bessa Monteiro, Universidade de Lisboa, em curso.
Orientações de teses de mestrado
- Enide Cascais Silva Andrade Martins, Os Valores Próprios de \([X,A]\), Universidade de Lisboa, concluída em 4 de Novembro 1994.
- Helena Marilde Cardoso, Completação de uma Submatriz Arbitrária, Universidade de Lisboa, concluída em 30 de Maio 1997.
- Maria Cristina Canelas Lopes Ferreira, Estabilidade Matricial, Universidade de Lisboa, concluída em 17 de Janeiro 2000.
- Laura Cristina Teixeira Iglésias, Generalização de Fórmulas Min-Max e Teoremas de Entrelaçamento, Universidade de Lisboa, concluída em 28 de Fevereiro 2000.
- Rita Isabel Gonçalves Simões, Partição Característica Sujeita a Pequenas Perturbações, Universidade de Lisboa, concluída em 21 de Maio 2003.
- Paulo Alexandre Barbosa de Matos Firmino, Fatores Invariantes de Produtos e Somas de Matrizes, Universidade de Lisboa, 21 de dezembro de 2021.
- (co-orientada por Jorge Nélio Marques Ferreira) Laura Santos Silva, Bases de Gröbner: Uma Introdução à Álgebra Comutativa Computacional, em curso, Universidade de Lisboa.
Artigos de investigação
- On a conjecture about rational valued characters, Linear
and Multilinear Algebra 15 (1984), 257-263.
- On the number of invariant polynomials of the matrix \(XAX^{-1}+B\), Linear
Algebra and Its Applications 79 (1986), 1-21.
- Matrices with prescribed eigenvalues and principal submatrices, Linear
Algebra and Its Applications 92 (1987), 241-250.
- Matrices with prescribed characteristic polynomial and submatrices, Portugaliæ
Mathematica 44 (1987), 261-264.
- On the invariant factors of the matrix \(XAY+B\), Linear
Algebra and Its Applications 96 (1987), 1-16.
- The eigenvalues of the sum of matrices with prescribed invariant polynomials, Linear and Multilinear
Algebra 22 (1987), 7-13.
- Weakly polynomially complete pairs of matrices, Linear
and Multilinear Algebra 22 (1987), 15-23.
- Spectrally complete pairs of matrices, Linear
Algebra and Its Applications 108 (1988), 239-262.
- The eigenvalues of the sum of matrices with prescribed invariant polynomials
II, Linear and
Multilinear Algebra 24 (1988), 45-49.
- The rank of the difference of matrices with prescribed invariant factors, Linear and Multilinear
Algebra 24 (1988), 59-63.
- The rank of the difference of matrices with prescribed similarity classes, Linear and Multilinear
Algebra 24 (1988), 51-58.
- Matrices with prescribed similarity class and a prescribed nonprincipal submatrix, Portugaliæ Mathematica 47 (1990),103-113.
- Sums and products of matrices with prescribed similarity classes, Linear
and Multilinear Algebra 27 (1990), 317-323.
- An additive inverse characteristic polynomial theorem, Portugaliæ
Mathematica 47 (1990), 403-409.
- Matrices with nonzero entries, Linear
Algebra and Its Applications 146 (1991), 111-119.
- Matrices with prescribed eigenvalues and blocks, Linear
Algebra and Its Applications 148 (1991), 59-73.
- (Em colaboração com Isabel Cabral) Unified theorems on completions of matrix pencils, Linear
Algebra and Its Applications 159 (1991), 43-54.
- (Em colaboração com Isabel Cabral) Similarity invariants of completions of submatrices, Linear Algebra and Its Applications 169 (1992), 151-161.
- Matrices with prescribed lower triangular part, Linear
Algebra and Its Applications 182 (1993), 27-34.
- The eigenvalues of the product of matrices with prescribed similarity classes, Linear and Multilinear
Algebra 34 (1993), 269-277.
- On the number of invariant polynomials of partially prescribed matrices, Linear
Algebra and Its Applications 197/198 (1994), 709-754.
- (Em colaboração com Isabel Cabral) Controllability indices of partially prescribed pairs of
matrices, Portugaliæ Mathematica 52 (1995), 175-192.
- (Em colaboração com Enide A. Martins) Eigenvalues of matrix commutators, Linear
and Multilinear Algebra 39 (1995), 375-389.
- On controllability of partially prescribed matrices, Linear
and Multilinear Algebra 40 (1995), 95-102.
- Integral representations of graphs, Portugaliæ
Mathematica 53 (1996), 137-142.
- Possible block similarity classes of a matrix with a prescribed nonprincipal
submatrix, Linear Algebra
and Its Applications 249 (1996), 359-373.
- (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.
- (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.
- (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.
- On a conjecture about the Jordan form of completions of partial upper triangular
matrices, Linear Algebra
and Its Applications 260 (1997), 319-321.
- (Em colaboração com Enide A. Martins) On the number of invariant polynomials of matrix commutators, Linear Algebra and Its
Applications 262 (1997), 179-188.
- Possible block similarity classes of a matrix with a prescribed nonprincipal
submatrix, II, Linear Algebra
and Its Applications 262 (1997), 259-282.
- On feedback equivalence and completion problems, Linear
Algebra and Its Applications 265 (1997), 231-245.
- (Em colaboração com Maria M. Torres) Rank partitions under small perturbations, Linear
and Multilinear Algebra 43 (1997), 299-313.
- (Em colaboração com Catarina Santa-Clara) On infinite Goldie dimension, Journal
of Algebra 205 (1998), 617-625.
- (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.
- Invariant polynomials of matrices with prescribed entries, Linear
and Multilinear Algebra 44 (1998), 357-372.
- (Em colaboração com Susana Furtado) On the characteristic polynomial of matrices with prescribed
rows, Linear Algebra and
Its Applications 293 (1999), 51-72.
- (Em colaboração com Orlando Neto) On the recognition and rigidity problems for sums of matrices, Linear Algebra and Its
Applications 293 (1999), 73-84.
- (Em colaboração com Susana Furtado) Embedding a regular subpencil into a general linear pencil, Linear Algebra and Its
Applications 295 (1999), 61-72.
- On the eigenvalues of matrices with prescribed upper triangular part, Linear
and Multilinear Algebra 46 (1999), 117-138.
- (Em colaboração com Orlando Neto) Singular regular differential equations and eigenvalues of
products of matrices, Linear
and Multilinear Algebra 46 (1999), 145-164.
- On the number of invariant factors of partially prescribed matrices and control
theory, Linear Algebra
and Its Applications 311 (2000), 1-12.
- (Em colaboração com Glória Cravo) Eigenvalues of matrices with several prescribed blocks, Linear Algebra and Its
Applications 311 (2000), 13-24.
- (Em colaboração com João Araújo) Semigroups of linear endomorphisms closed under
conjugation, Communications
in Algebra 28 (2000), 3679-3689.
- (Em colaboração com Isabel T. Matos) A completion problem over the field of real numbers, Linear Algebra and Its Applications 320 (2000), 63-77.
- (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.
- (Em colaboração com Susana Furtado and Enide A. Martins) On similarity invariants of matrix
commutators, Linear Algebra
and Its Applications 335 (2001), 81-93.
- (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.
- (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.
- (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.
- (Em colaboração com Enide A. Martins) On the eigenvalues of Jordan products, Linear
Algebra and Its Applications 359 (2003), 249-262.
- (Em colaboração com Enide A. Martins) On the invariant polynomials of Jordan products, Linear
Algebra and Its Applications 360 (2003), 173-189.
- (Em colaboração com Glória Cravo) Eigenvalues of matrices with several prescribed blocks
II, Linear Algebra and
Its Applications 364 (2003), 81-89.
- (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.
- (Em colaboração com Jaspal Singh Aujla) Weak majorization inequalities and convex functions, Linear Algebra and Its
Applications 369 (2003), 217-233.
- (Em colaboração com Cristina Ferreira) Inertia theorems for pairs of matrices, Linear
Algebra and Its Applications 381 (2004), 37-52.
- (Em colaboração com Cristina Ferreira) On the stabilization of linear discrete-time systems, Linear Algebra and Its
Applications 390 (2004), 7-18.
- (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.
- (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.
- (Em colaboração com Cristina Ferreira) Inertia theorems for pairs of matrices, II, Linear
Algebra and Its Applications 413 (2006), 425-439.
- (Em colaboração com Susana Furtado and Laura Iglésias), Eigenvalues of products of matrices, Linear and Multilinear
Algebra, 54 (2006), 343-353.
- (Em colaboração com Rita Simões) On the Lyapunov and Stein equations, Linear Algebra and Its Applications 420 (2007), 329-338.
- (Em colaboração com Rita Simões) On the Lyapunov and Stein equations, II, Linear Algebra and Its Applications 426 (2007), 305-311.
- (Em colaboração com Marija Dodig) Controllability of series connections of arbitrarily many linear systems, Linear Algebra and Its Applications 429 (2008), 122-141.
- (Em colaboração com Isabel T. Matos) Completion problems for real matrices, II, Linear Algebra and Its Applications 432 (2010), 180202.
- (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.
- (Em colaboração com Rita Simões) Row and column rank partitions under small perturbations, Linear
and Multilinear Algebra 60 (2012), 1-9.
- (Em colaboração com Alicia Roca) Pencils with prescribed constant subpencils, Linear Algebra and Its Applications 436 (2012), 33153336.
- (Em colaboração com Alicia Roca) Pencils with prescribed constant subpencils over arbitrary fields, Linear Algebra and Its Applications 445 (2014), 138161.
- (Em colaboração com Maria da Graça Duffner) On the interlacing inequalities for invariant factors, Linear Algebra and Its Applications 486 (2015), 443-448.
- (Em colaboração com Laura Iglésias) Spectral and weak polynomial completeness for the product of nonsingular matrices, Linear
and Multilinear Algebra 63 (2015), 1937-1946.
- (Em colaboração com Laura Iglésias) Weakly spectrally complete pair of matrices, Linear
and Multilinear Algebra 64 (2016), 942-950.
- (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.
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