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He obtained his PhD in Sciences (Mathematics) in 2002 supervised by Roland Puystjens (University of Ghent, Belgium), his MSc in Mathematics in 1998 from the University of Coimbra and his BSc in Mathematics (Pure Mathematics) in 1995 from the University of Coimbra. He is an Associate Professor with Habilitation at the University of Minho. As in August 2024, he has published 54 articles in specialised journals with 980 citations and h-index 19. Supervised 1 doctoral thesis and co-supervised 3. Supervised 16 master's theses. He was a Principal Investigator in 1 project. He works in the area of Mathematics with an emphasis on Matrix Theory. In his professional activities he has interacted with 40 collaborators in co-authoring scientific work. He has been supervising dissertations in cryptography, post quantum cryptography, coding theory, quantum error correcting codes, modelling and simulation, applications of neural networks, electronic voting, to name a few. He has held several managment responsabilities; member of the directive committee of the department, head of studies of the BSc in Computer Sciences, of the MSc in Mathematics and Computation, Director of the research center CMAT. He has presented more than 20 talks in the scope of outreach activities, and a large number of scientific talks (seminars, talks in scientific meetings). He has served as referee for many scientific journals, namely Linear Algebra and Its Applications, Linear and Multilinear Algebra, Electronic Journal of Linear Algebra, Applied Maths and Computation, Semigroup Forum, Journal of Algebra and Applications. He was a editor for Boletim da Sociedade Portuguesa de Matematica. He is now a member of the board of Sociedade Portuguesa de Matematica.
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Identification

Personal identification

Full name
Pedro Patrício

Citation names

  • Patrício, Pedro

Author identifiers

Ciência ID
AA10-016D-2825
ORCID iD
0000-0001-9776-0919
Google Scholar ID
https://scholar.google.com/citations?user=Yxf3NgUAAAAJ&hl=en&oi=ao
Researcher Id
M-8569-2018
Scopus Author Id
6701711621

Websites

Knowledge fields

  • Exact Sciences - Mathematics - Pure Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
English Advanced (C1) Advanced (C1) Advanced (C1) Advanced (C1) Advanced (C1)
French Upper intermediate (B2) Upper intermediate (B2) Intermediate (B1) Upper intermediate (B2) Intermediate (B1)
Portuguese (Mother tongue)
Education
Degree Classification
2024/06/27
Concluded
 Matemática (Título de Agregado)
Universidade do Minho, Portugal
 Aprovado por unanimidade
2002
Concluded
 Doutoramento em Ciências (Esp. Matemática) (Doutoramento)
Universidade do Minho Escola de Ciências, Portugal
"Uma contribuição para a teoria algébrica da invertibilidade generalizada" (THESIS/DISSERTATION)
 Aprovado
1998
Concluded
 Mestrado em Matemática (Mestrado)
Universidade de Coimbra Faculdade de Ciencias e Tecnologia, Portugal
"Convexidade e sistemas de decomposição normal" (THESIS/DISSERTATION)
 Bom
1995
Concluded
 Licenciatura em Matemática (Ramo Científico - Esp. Matemática Pura) (Licenciatura)
Universidade de Coimbra Faculdade de Ciencias e Tecnologia, Portugal
 bom
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
2021/02/11 - Current Associate Professor (University Teacher) Universidade do Minho, Portugal
2002/12/10 - 2021/02/10 Assistant Professor (University Teacher) Universidade do Minho, Portugal
2013 - 2019 Assistant Professor (University Teacher) Universidade do Minho, Portugal
2013 - 2019 Assistant Professor (University Teacher) Universidade do Minho, Portugal
2013 - 2019 Assistant Professor (University Teacher) Universidade do Minho, Portugal
2002 - 2019 Assistant Professor (University Teacher) Universidade do Minho, Portugal

Positions / Appointments

Category
Host institution 		Employer
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
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
2017 - 2018 Coordenação ou direção de centro de investigação, departamento ou equivalente Universidade do Minho, Portugal
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 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
2017 - 2018 Coordenação ou direção de centro de investigação, departamento ou equivalente Universidade do Minho, Portugal
2017 - 2018 Conselho de gestão ou orgão correspondente Universidade do Minho, Portugal
2017 - 2018 Conselho científico/técnico-científico ou orgão correspondente Universidade do Minho, Portugal
2017 - 2018 Coordenação ou direção de centro de investigação, departamento ou equivalente Universidade do Minho, Portugal
2017 - 2018 Conselho de gestão ou orgão correspondente Universidade do Minho, Portugal
2017 - 2018 Conselho científico/técnico-científico ou orgão correspondente Universidade do Minho, Portugal
Projects

Contract

Designation Funders
2020/01/01 - 2023/12/31 Centro de Matemática da Universidade do Minho
UIDB/00013/2020
10.54499/UIDB/00013/2020
Researcher
Universidade do Minho, Portugal

Universidade do Minho Centro de Matemática, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2020/01/01 - 2023/12/31 Centro de Matemática da Universidade do Minho
UIDP/00013/2020
10.54499/UIDP/00013/2020
Universidade do Minho, Portugal

Universidade do Minho Centro de Matemática, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2021/11/01 - 2023/10/31 Inclusive mathematics education based on digital learning
2021-1-FR01-KA220-HED-000023486
Researcher
2021/01/01 - 2023/06/30 BREUCA
C30/2020/48257
Principal investigator
Instituto Politécnico de Tomar, Portugal

Universidade do Minho, Portugal
Agência Nacional de Inovação SA
2011/01/01 - 2013/12/31 Projecto Estratégico - UI 13 - 2011-2012
PEst-C/MAT/UI0013/2011
Universidade do Minho, Portugal

Universidade do Minho Centro de Matemática, Portugal
Fundação para a Ciência e a Tecnologia
Concluded

Other

Designation Funders
2021/07/30 - Current UID 13 - Centro de Matemática da Universidade do Minho (CMAT)
7/2021/50
Universidade do Minho, Portugal
 Fundação para a Ciência e a Tecnologia
Outputs

Publications

Journal article
  1. Zhu, H.; Xu, D.; Patrício, P.; Mosic, D.. "The (B, C)-Core inverse of rectangular matrices". Quaestiones Mathematicae (2024): http://www.scopus.com/inward/record.url?eid=2-s2.0-85200043722&partnerID=MN8TOARS.
    10.2989/16073606.2024.2374776
  2. Robert E. Hartwig; Pedro Patrício. "Divisibility of Finite Geometric Series". Bulletin of the Malaysian Mathematical Sciences Society (2023): https://doi.org/10.1007/s40840-023-01556-5.
    10.1007/s40840-023-01556-5
  3. Hartwig, R.E.; Patrício, P.. "The GCD for finite geometric series". Filomat 37 29 (2023): 9973-9979. http://www.scopus.com/inward/record.url?eid=2-s2.0-85196617028&partnerID=MN8TOARS.
    10.2298/FIL2329973H
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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
  32. 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.
  33. 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
  34. 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
  35. 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
  36. 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.
  37. 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
  38. 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
  39. 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.
  40. 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
  41. 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
  42. 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
  43. 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
  44. 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
  45. 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
  46. 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
  47. 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.
  48. 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
  49. 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
  50. 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
  51. 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
  52. 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
  53. 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
  54. 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

Other

Other output
  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-s2.0-85169282447&partnerID=MN8TOARS.
    10.48550/arxiv.1805.08696
  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-s2.0-85170296534&partnerID=MN8TOARS.
    10.48550/arxiv.1803.10186
  3. Computação: "The unreasonable effectiveness of mathematics in the computer/natural sciences". O conjunto de conteúdos "Computação - 'The Unreasonable Effectiveness of Mathematics in the Computer Sciences' " é de autoria de uma equipa de docentes do Departamento de Matemática e Aplicações e foi produzido originalmente para ser apresentado na Noite Europeia dos Investigadores de 2016, que decorreu a 30 de Setembro, no Museu D. Diogo de Sousa em Braga, tendo o conjunto sido apresentado nessa. 2016. Espírito Santo, José; Araújo, Cláudia Mendes; Forjaz, Maria Antónia; Martins, Paula Mendes; Patrício, Pedro; Pinto, Luís F.; Ralha, Rui. http://hdl.handle.net/1822/58175.
  4. Grafos e digrafos com o sagemath. Texto de apoio a parte da Acção de Formação em Grafos, com uso de Maxima e Sagemath.. Breve introdução ao digrafos com auxílio do SageMath.. 2008. Patrício, Pedro. http://hdl.handle.net/1822/18790.
  5. Teoria de números computacional visto pelos olhos do Pari/GP. Notas de apoio para Teoria de Números Computacional, LCC&LMat. Nestas notas pretendemos exemplificar algumas formas de aplicar a Teoria de Números Computacional num CAS, e em particular no Pari/GP. Estas notas não substituem as que por ventura retirará das aulas teóricas. Deve, sempre que possível, experimentar por si as informações descritas neste documento.. 2008. Patrício, Pedro. http://hdl.handle.net/1822/18791.
  6. Introdução à álgebra linear com o gnu-Octave. Texto de apoio para Álgebra Linear C (Mestrado Integrado em Engenharia Biológica), com o gnu-Octave.. 2007. Patrício, Pedro. http://hdl.handle.net/1822/18793.
  7. Códigos lineares com o Mu-pad: notas de apoio para teoria de códigos. Notas de apoio para Teoria de Códigos, fazendo uso do MuPad.. 2005. Patrício, Pedro. http://hdl.handle.net/1822/18792.
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2022/06 On the group inverse of a product 9th International Conference on Matrix Analysis and Applications (ICMAA 2022)
(Aveiro, Portugal)
2022 From Brown-McCoy to orthogonality ALC Meeting 2022
CMAT (Braga, Portugal)
2021 On the Group Inverse of Some Kronecker Sums MS Generalized Inverses, Operator and Quaternion Equations, Conference on Applied Linear Algebra
online
2021 Stabilizer Formalism for Error Correction ALC Meeting
CMAT (Braga, Portugal)
2019 The Group Inverse of the Nivellateur International Meeting on Generalized Inverses and Its Applications
Hubei Normal University (Hubei, China)
2018/06 The Group Inverse of the Nivellateur WOTCA 2018
Guimarães (Guimarães, Portugal)
2013/07 The group inverse of a matrix International Workshop on Matrix Theory and Ring Theory
Southeast University (Nanjing, China)
2013/07 Generalized invertibility of block matrices 1-day Workshop in Algebra
Nanjing University (Nanjing, China)
2012 Generalised inverses and path products SIAM Meeting
SIAM (Valencia, Spain)
2010 Additive Drazin inverses 16th ILAS Conference
ILAS (Pisa, Italy)

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2023 - Current Machine Learning of Quantum Circuit Layouts
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2023 - Current On generalized inverses of graph matrices
Supervisor
 MAP-PDMA PhD programme (PhD)
Universidade do Minho, Portugal
2022 - Current Data privacy for NoSQL databases and Machine Learning
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2022 - Current Construction of synthetic track data for the minimum lap time simulation problem
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2022 - Current Computer-assisted proofs for matrix identities through Grobner bases
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2021 - Current Experimentation with post-quantum cryptographic algorithms: the CRYSTALS case
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2021 - Current Quantum error correcting codes
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2020 - Current Matchgate circuits with magic resources for universal quantum computation
Co-supervisor
 MAP-PDMA PhD programme (PhD)
Universidade do Minho, Portugal
2019 - Current Post-quantum cryptosystems
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2016 - Current Generalised inverses in rings and semigroups
Co-supervisor
Southeast University School of Mathematics, China
2023 - 2023 Modelação Matemática para a inspeção de materiais naturais - caso de estudo pele natural
Supervisor
 Matemática e Computação (Master)
Universidade do Minho, Portugal
2019 - 2021 Quantum Error Correcting Codes
Supervisor
 MSc in Physics Engineering (Master)
Universidade do Minho, Portugal
2019 - 2020 Experimentation of Hybrid Certificates with Post-quantum Cryptography
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2018 - 2019 A cryptographic approach to electoral systems
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2017 - 2017 Modelação com técnicas de clustering de participações geoespaciais de cidadãos Matemática e Computação (Master)
Universidade do Minho, Portugal
2017 - 2017 An algebraic approach to Convolutional Codes Matemática (Master)
Universidade do Minho, Portugal
2016 - 2017 Secure Transactions with Blockchains
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2014 - 2016 The study of generalised inverses in rings
Co-supervisor
Southeast University School of Mathematics, China
2015 - 2015 Public Keys Quality
Supervisor
 Matemática e Computação (Master)
Universidade do Minho, Portugal
2011 - 2012 Implementation of hash functions and public key ciphers based on lattices
Supervisor
 MSc in Mathematics and Computation (Master)
Universidade do Minho, Portugal
2006 - 2008 Algebraic Theory of Generalised Inverses
Supervisor
 MSc in Mathematics (Master)
Universidade do Minho, Portugal
2004 - 2006 Elements of Cryptography: an application of Algebra
Supervisor
 MSc in Mathematics (Master)
Universidade do Minho, Portugal

Event organisation

Event name
Type of event (Role) 		Institution / Organization
2019/04 - 2019/04 QDays workshop on quantum computing (2019/04 - 2019/04)
Meeting
 Universidade do Minho, Portugal
2010/10 - 2010/10 III Iberian Mathematical Meeting (2010 - 2010)
Congress (Member of the Organising Committee)

Committee member

Activity description
Role 		Institution / Organization
2022/06 - 2024/06 Managment Board of Sociedade Portuguesa de Matemática
Member
 Sociedade Portuguesa de Matemática, Portugal
2010/06 - 2010/06 Mini-symposium on Generalized Inverses and Applications, ILAS, Pisa, 2010
Coordinator
 The International Linear Algebra Society, United States