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Pedro Patrício. Concluiu o(a) Doutoramento em Ciências em 2002/12/10 pelo(a) Universidade do Minho. É Professor Auxiliar no(a) Universidade do Minho. Publicou 45 artigos em revistas especializadas. Nas suas atividades profissionais interagiu com 27 colaborador(es) em coautorias de trabalhos científicos.
Identificação

Identificação pessoal

Nome completo
Pedro Patrício

Nomes de citação

  • Patrício, Pedro

Identificadores de autor

Ciência ID
AA10-016D-2825
ORCID iD
0000-0001-9776-0919
Formação
Grau Classificação
2002/12/10
Concluído
Ciências (Doutoramento)
Especialização em Matemática
Universidade do Minho, Portugal
"Uma Contribuição para a Teoria Algébrica da Invertibilidade Generalizada" (TESE/DISSERTAÇÃO)
2002
Concluído
Doutoramento em Ciências (Esp. Matemática) (Doutoramento)
Universidade do Minho Escola de Ciências, Portugal
"Uma contribuição para a teoria algébrica da invertibilidade generalizada" (TESE/DISSERTAÇÃO)
Aprovado
1998
Concluído
Mestrado em Matemática (Mestrado)
Universidade de Coimbra Faculdade de Ciencias e Tecnologia, Portugal
"Convexidade e sistemas de decomposição normal" (TESE/DISSERTAÇÃO)
Bom
1995
Concluído
Licenciatura em Matemática (Ramo Científico - Esp. Matemática Pura) (Licenciatura)
Universidade de Coimbra Faculdade de Ciencias e Tecnologia, Portugal
bom
Percurso profissional

Docência no Ensino Superior

Categoria Profissional
Instituição de acolhimento
Empregador
2021/02/11 - Atual Professor Associado (Docente Universitário) Universidade do Minho, Portugal
2002/12/10 - 2021/02/10 Professor Auxiliar (Docente Universitário) Universidade do Minho, Portugal

Cargos e Funções

Categoria Profissional
Instituição de acolhimento
Empregador
2017 - 2018 Conselho científico/técnico-científico ou orgão correspondente Universidade do Minho, Portugal
2017 - 2018 Conselho de gestão ou orgão correspondente Universidade do Minho, Portugal
2017 - 2018 Coordenação ou direção de centro de investigação, departamento ou equivalente Universidade do Minho, Portugal
Produções

Publicações

Artigo em revista
  1. Huihui Zhu; Liyun Wu; Fei Peng; Pedro Patrício. "Characterizations and representations of left and right hybrid (b, c)-inverses in rings". Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 115 1 (2021): https://doi.org/10.1007/s13398-020-00956-7.
    10.1007/s13398-020-00956-7
  2. Gao, Y.; Chen, J.; Patrício, P.. "Continuity of the core-EP inverse and its applications". Linear and Multilinear Algebra 69 3 (2021): 557-571. http://www.scopus.com/inward/record.url?eid=2-s2.0-85065105646&partnerID=MN8TOARS.
    10.1080/03081087.2019.1608899
  3. Patrício, P.; Hartwig, R.E.. "From Euclid to Corner Sums – a Trail of Telescoping Tricks". Filomat 35 14 (2021): 4613-4636. http://www.scopus.com/inward/record.url?eid=2-s2.0-85126305839&partnerID=MN8TOARS.
    10.2298/FIL2114613P
  4. Mary, X.; Patrício, P.. "Characterizations of special clean elements and applications". Filomat 34 14 (2020): 4847-4860. http://www.scopus.com/inward/record.url?eid=2-s2.0-85103646229&partnerID=MN8TOARS.
    10.2298/FIL2014847M
  5. Gao, Y.; Chen, J.; Patrício, P.. "Weighted binary relations involving core-EP inverse". Frontiers of Mathematics in China 15 4 (2020): 685-699. http://www.scopus.com/inward/record.url?eid=2-s2.0-85090015197&partnerID=MN8TOARS.
    10.1007/s11464-020-0856-7
  6. Huihui Zhu; Pedro Patrício. "Several types of one-sided partial orders in rings". Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (2019): https://doi.org/10.1007/s13398-019-00685-6.
    10.1007/s13398-019-00685-6
  7. Mary, X.; Patrício, P.. "Group-regular rings". Filomat 33 11 (2019): 3551-3560. http://www.scopus.com/inward/record.url?eid=2-s2.0-85077673673&partnerID=MN8TOARS.
    10.2298/FIL1911551M
  8. Honglin Zou; Jianlong Chen; Pedro Patrício. "Reverse Order Law for the Core Inverse in Rings". Mediterranean Journal of Mathematics 15 3 (2018): https://doi.org/10.1007/s00009-018-1189-6.
    10.1007/s00009-018-1189-6
  9. Gao, Y.; Chen, J.; Patrício, P.; Wang, D.. "The pseudo core inverse of a companion matrix". Studia Scientiarum Mathematicarum Hungarica 55 3 (2018): 407-420. http://www.scopus.com/inward/record.url?eid=2-s2.0-85055136379&partnerID=MN8TOARS.
    10.1556/012.2018.55.3.1398
  10. Zhu, H.; Zou, H.; Patrício, P.. "Generalized inverses and their relations with clean decompositions". Journal of Algebra and its Applications (2018): http://www.scopus.com/inward/record.url?eid=2-s2.0-85053043828&partnerID=MN8TOARS.
    10.1142/S0219498819501330
  11. Zhu, H.; Patrício, P.. "Characterizations for pseudo core inverses in a ring with involution". Linear and Multilinear Algebra (2018): 1-12. http://www.scopus.com/inward/record.url?eid=2-s2.0-85044057293&partnerID=MN8TOARS.
    10.1080/03081087.2018.1446506
  12. Zhu, H.; Patrício, P.. "A note on clean elements and inverses along an element". Filomat 32 12 (2018): 4285-4290. http://www.scopus.com/inward/record.url?eid=2-s2.0-85061335713&partnerID=MN8TOARS.
    10.2298/FIL1812285Z
  13. Gao, Y.; Chen, J.; Patrício, P.. "Representations and properties of the W-weighted core-EP inverse". Linear and Multilinear Algebra (2018): http://www.scopus.com/inward/record.url?eid=2-s2.0-85055564403&partnerID=MN8TOARS.
    10.1080/03081087.2018.1535573
  14. Hartwig, R.E.; Patrício, P.. "Invariance under outer inverses". Aequationes Mathematicae (2017): 1-9. http://www.scopus.com/inward/record.url?eid=2-s2.0-85039840125&partnerID=MN8TOARS.
    10.1007/s00010-017-0524-5
  15. Zou, H.; Chen, J.; Patrício, P.. "Characterizations of m-EP elements in rings". Linear and Multilinear Algebra (2017): 1-13. http://www.scopus.com/inward/record.url?eid=2-s2.0-85022202623&partnerID=MN8TOARS.
    10.1080/03081087.2017.1347136
  16. Chen, J.; Zou, H.; Zhu, H.; Patrício, P.. "The One-Sided Inverse Along an Element in Semigroups and Rings". Mediterranean Journal of Mathematics 14 5 (2017): http://www.scopus.com/inward/record.url?eid=2-s2.0-85029892081&partnerID=MN8TOARS.
    10.1007/s00009-017-1017-4
  17. Hartwig, R.E.; Patrício, P.. "The group inverse of the nivellateur". Linear and Multilinear Algebra (2017): 1-12. http://www.scopus.com/inward/record.url?eid=2-s2.0-85033674284&partnerID=MN8TOARS.
    10.1080/03081087.2017.1397092
  18. Zhu, H.; Chen, J.; Patrício, P.; Mary, X.. "Centralizer's applications to the inverse along an element". Applied Mathematics and Computation 315 (2017): 27-33. http://www.scopus.com/inward/record.url?eid=2-s2.0-85026345295&partnerID=MN8TOARS.
    10.1016/j.amc.2017.07.046
  19. Jianlong Chen; Pedro Patricio; Yulin Zhang; Huihui Zhu; Chen, J.; Zhu, H.; Patricio, P.; Zhang, Y.. "Characterizations and representations of core and dual core inverses". Bulletin canadien de mathématiques 60 2 (2016): 1-19. https://doi.org/10.4153%2Fcmb-2016-045-7.
    10.4153/cmb-2016-045-7
  20. Huihui Zhu; Jianlong Chen; Pedro Patrício. "Reverse order law for the inverse along an element". Linear and Multilinear Algebra 65 1 (2016): 166-177. https://doi.org/10.1080%2F03081087.2016.1178209.
    10.1080/03081087.2016.1178209
  21. Zhu, H.; Patrício, P.; Chen, J.; Zhang, Y.. "The inverse along a product and its applications". Linear and Multilinear Algebra 64 5 (2016): 834-841. http://www.scopus.com/inward/record.url?eid=2-s2.0-84935417372&partnerID=MN8TOARS.
    10.1080/03081087.2015.1059796
  22. Zhu, H.; Chen, J.; Patrício, P.. "The Moore-Penrose inverse of differences and products of projectors in a ring with involution". Turkish Journal of Mathematics 40 6 (2016): 1316-1324. http://www.scopus.com/inward/record.url?eid=2-s2.0-85007189916&partnerID=MN8TOARS.
    10.3906/mat-1405-1
  23. Zhu, H.; Chen, J.; Patrício, P.. "Further results on the inverse along an element in semigroups and rings". Linear and Multilinear Algebra 64 3 (2016): 393-403. http://www.scopus.com/inward/record.url?eid=2-s2.0-84953357073&partnerID=MN8TOARS.
    10.1080/03081087.2015.1043716
  24. Mary, X.; Patrício, P.. "The group inverse of a product". Linear and Multilinear Algebra 64 9 (2016): 1776-1784. http://www.scopus.com/inward/record.url?eid=2-s2.0-84951291697&partnerID=MN8TOARS.
    10.1080/03081087.2015.1120265
  25. Burgos, M.; Márquez-García, A.C.; Patrício, P.. "On mappings preserving the sharp and star orders". Linear Algebra and Its Applications 483 (2015): 268-292. http://www.scopus.com/inward/record.url?eid=2-s2.0-84935002184&partnerID=MN8TOARS.
    10.1016/j.laa.2015.05.003
  26. Zhu, H.; Chen, J.; Patrício, P.. "Representations for the pseudo Drazin inverse of elements in a Banach algebra". Taiwanese Journal of Mathematics 19 2 (2015): 349-362. http://www.scopus.com/inward/record.url?eid=2-s2.0-84925351829&partnerID=MN8TOARS.
    10.11650/tjm.19.2015.4576
  27. Patrício, P.; Hartwig, R.E.. "Some regular sums". Linear and Multilinear Algebra 63 1 (2015): 185-200. http://www.scopus.com/inward/record.url?eid=2-s2.0-84908546178&partnerID=MN8TOARS.
    10.1080/03081087.2013.860592
  28. Zhu, H.; Chen, J.; Zhang, X.; Patrício, P.. "The Moore-Penrose inverse of 2 × 2 matrices over a certain *-regular ring". Applied Mathematics and Computation 246 (2014): 263-267. http://www.scopus.com/inward/record.url?eid=2-s2.0-84907190553&partnerID=MN8TOARS.
    10.1016/j.amc.2014.08.026
  29. Hartwig, R.E.; Patrício, P.. "Two by two units". Electronic Journal of Linear Algebra 27 (2014): 489-503. http://www.scopus.com/inward/record.url?eid=2-s2.0-84905440207&partnerID=MN8TOARS.
  30. Lebtahi, L.; Patrício, P.; Thome, N.. "The diamond partial order in rings". Linear and Multilinear Algebra 62 3 (2014): 386-395. http://www.scopus.com/inward/record.url?eid=2-s2.0-84893557133&partnerID=MN8TOARS.
    10.1080/03081087.2013.779272
  31. Lebtahi, L.; Patrício, P.; Thome, N.. "Special elements in a ring related to Drazin inverses". Linear and Multilinear Algebra 61 8 (2013): 1017-1027. http://www.scopus.com/inward/record.url?eid=2-s2.0-84880275304&partnerID=MN8TOARS.
    10.1080/03081087.2012.728598
  32. Mary, X.; Patrício, P.. "Generalized inverses modulo H in semigroups and rings". Linear and Multilinear Algebra 61 8 (2013): 1130-1135. http://www.scopus.com/inward/record.url?eid=2-s2.0-84880302365&partnerID=MN8TOARS.
    10.1080/03081087.2012.731054
  33. Hartwig, R.E.; Patricio, P.. "When does the moore-penrose inverse flip?". Operators and Matrices 6 1 (2012): 181-192. http://www.scopus.com/inward/record.url?eid=2-s2.0-84555203695&partnerID=MN8TOARS.
  34. Mary, X.; Patrício, P.. "The inverse along a lower triangular matrix". Applied Mathematics and Computation 219 3 (2012): 886-891. http://www.scopus.com/inward/record.url?eid=2-s2.0-84867336890&partnerID=MN8TOARS.
    10.1016/j.amc.2012.06.060
  35. Patrício, P.; Hartwig, R.E.. "The (2,2,0) Drazin inverse problem". Linear Algebra and Its Applications 437 11 (2012): 2755-2772. http://www.scopus.com/inward/record.url?eid=2-s2.0-84865675157&partnerID=MN8TOARS.
    10.1016/j.laa.2012.07.008
  36. Hartwig, R.E.; Patricio, P.. "A note on power bounded matrices". Electronic Journal of Linear Algebra 23 (2012): 625-645. http://www.scopus.com/inward/record.url?eid=2-s2.0-84908257572&partnerID=MN8TOARS.
  37. Patrício, P.. "The Moore-Penrose inverse of a companion matrix". Linear Algebra and Its Applications 437 3 (2012): 870-877. http://www.scopus.com/inward/record.url?eid=2-s2.0-84861101059&partnerID=MN8TOARS.
    10.1016/j.laa.2012.03.019
  38. Castro-González, N.; Mendes-Araújo, C.; Patricio, P.. "Generalized inverses of a sum in rings". Bulletin of the Australian Mathematical Society 82 1 (2010): 156-164. http://www.scopus.com/inward/record.url?eid=2-s2.0-77957342878&partnerID=MN8TOARS.
    10.1017/S0004972710000080
  39. Patrício, P.; Hartwig, R.E.. "The (2, 2, 0) group inverse problem". Applied Mathematics and Computation 217 2 (2010): 516-520. http://www.scopus.com/inward/record.url?eid=2-s2.0-77955655795&partnerID=MN8TOARS.
    10.1016/j.amc.2010.05.084
  40. Patrício, P.; Araújo, C.M.. "Moore-Penrose invertibility in involutory rings: The case aa†=bb†". Linear and Multilinear Algebra 58 4 (2010): 445-452. http://www.scopus.com/inward/record.url?eid=2-s2.0-77951908037&partnerID=MN8TOARS.
    10.1080/03081080802652279
  41. Patrício, P.; Hartwig, R.E.. "The link between regularity and strong-pi-regularity". Journal of the Australian Mathematical Society 89 1 (2010): 17-22. http://www.scopus.com/inward/record.url?eid=2-s2.0-78049265748&partnerID=MN8TOARS.
    10.1017/S1446788710001448
  42. Patrício, P.; Costa, A.V.. "On the Drazin index of regular elements". Central European Journal of Mathematics 7 2 (2009): 200-205. http://www.scopus.com/inward/record.url?eid=2-s2.0-66249133970&partnerID=MN8TOARS.
    10.2478/s11533-009-0015-6
  43. Patrício, P.; Hartwig, R.E.. "Some additive results on Drazin inverses". Applied Mathematics and Computation 215 2 (2009): 530-538. http://www.scopus.com/inward/record.url?eid=2-s2.0-68949163053&partnerID=MN8TOARS.
    10.1016/j.amc.2009.05.021
  44. Hartwig, R.E.; Patricio, P.. "On Roth's pseudo equivalence over rings". Electronic Journal of Linear Algebra 16 (2007): 111-124. http://www.scopus.com/inward/record.url?eid=2-s2.0-34248560968&partnerID=MN8TOARS.
  45. Hartwig, R.E.; Patrício, P.; Puystjens, R.. "Diagonalizing triangular matrices via orthogonal Pierce decompositions". Linear Algebra and Its Applications 401 1-3 (2005): 381-391. http://www.scopus.com/inward/record.url?eid=2-s2.0-16444387623&partnerID=MN8TOARS.
    10.1016/j.laa.2004.10.002
  46. Patrício, P.; Puystjens, R.. "Generalized invertibility in two semigroups of a ring". Linear Algebra and Its Applications 377 1-3 (2004): 125-139. http://www.scopus.com/inward/record.url?eid=2-s2.0-0242654066&partnerID=MN8TOARS.
    10.1016/j.laa.2003.08.004
  47. Patrício, P.; Puystjens, R.. "Drazin-Moore-Penrose invertibility in rings". Linear Algebra and Its Applications 389 1-3 (2004): 159-173. http://www.scopus.com/inward/record.url?eid=2-s2.0-4043176373&partnerID=MN8TOARS.
    10.1016/j.laa.2004.04.006
  48. Patrício, P.. "The Moore-Penrose inverse of a factorization". Linear Algebra and Its Applications 370 SUPP (2003): 227-235. http://www.scopus.com/inward/record.url?eid=2-s2.0-0038116166&partnerID=MN8TOARS.
    10.1016/S0024-3795(03)00391-4
  49. Koliha, J.J.; Patricio, P.. "Elements of rings with equal spectral idempotents". Journal of the Australian Mathematical Society 72 1 (2002): 137-152. http://www.scopus.com/inward/record.url?eid=2-s2.0-0036346975&partnerID=MN8TOARS.
    10.1017/S1446788700003657
  50. Patrício, P.. "The Moore-Penrose inverse of von Neumann regular matrices over a ring". Linear Algebra and Its Applications 332-334 (2001): 469-483. http://www.scopus.com/inward/record.url?eid=2-s2.0-0035427186&partnerID=MN8TOARS.
    10.1016/S0024-3795(01)00298-1
  51. Patrício, P.; Puystjens, R.. "About the von Neumann regularity of triangular block matrices". Linear Algebra and Its Applications 332-334 (2001): 485-502. http://www.scopus.com/inward/record.url?eid=2-s2.0-0035427099&partnerID=MN8TOARS.
    10.1016/S0024-3795(01)00295-6

Outros

Outra produção
  1. Continuity of the core-EP inverse and its applications. 2018. Gao, Y.; Chen, J.; Patrício, P.. http://www.scopus.com/inward/record.url?eid=2-s2.0-85094386787&partnerID=MN8TOARS.
  2. Representations and properties of the W-weighted core-EP inverse. 2018. Gao, Y.; Chen, J.; Patrício, P.. http://www.scopus.com/inward/record.url?eid=2-s2.0-85094299026&partnerID=MN8TOARS.
Atividades

Orientação

Título / Tema
Papel desempenhado
Curso (Tipo)
Instituição / Organização
2017 - 2017 Modelação com técnicas de clustering de participações geoespaciais de cidadãos Matemática e Computação (Mestrado)
Universidade do Minho, Portugal
2017 - 2017 An algebraic approach to Convolutional Codes Matemática (Mestrado)
Universidade do Minho, Portugal
2015 - 2015 Public Keys Quality Matemática e Computação (Mestrado)
Universidade do Minho, Portugal