[ scientific interests/teaching ]
[ publications ]
[ research colaboration ]
[ math stuff ]
[ non-math stuff ]
[ linux links ]
[ blog ]
my scientic interests are in the area of generalized inverses, thru
an algebraic approach. this includes g.i. of matrices over rings,
partial orderings, g.i. on rings and semigroups...
i did my PhD under supervision of Roland Puystjens, from the RUG, Gent,
Belgium. until he retired, we
continued to do some joint work. part of this work was jointly with R.E.
Hartwig, from NCSU, USA, with whom i have been
working. more recently, two colleagues from my department started to be
interested on generalized inverses, and eventually we submitted and got our papers accepted. one of these
results led to recent research colaboration with nieves castro-gonzalez.
in the meanwhile, among the several courses i taught, some caught my
real interest either by the way
they were taught, or by the course itself. these, occasionally, led to
some course notes.
other math interests include algebraic coding theory (block codes and
convolutional codes) and cryptography.
SOME courses i taught RECENTLY (and enjoyed)
- teoria de codigos - coding theory (with mupad) (2005/06)
- matematica discreta - discrete mathematics (2005/06)
- algebra linear (para engenheiros) - linear algebra (with octave)
- teoria de numeros computacional - computational number theory (with
pari/gp) (2006/07, 2008/09)
Make the Move!
Windows to Linux
list of publications
- Patricio, P., The Moore-Penrose inverse of von Neumann regular
matrices over a ring, Linear Algebra and Its Applications,
- Patricio, P. and Puystjens, R., About the von Neumann regularity
of triangular block matrices, Linear Algebra and Its Applications,
- Koliha, J.J. and Patricio, P., Elements of rings with equal
spectral idempotents, Journal of the Australian Mathematical Society,
- Patricio, P., The Moore-Penrose inverse of a factorization,
Linear Algebra and Its Applications, 370:227-235, 2003.
- P. Patricio and R. Puystjens, Generalized invertibility in two
semigroups of a ring, Linear Algebra and Its Applications, 377:125-139,
- P. Patricio and R. Puystjens, Drazin-Moore-Penrose invertibility
in rings, Linear Algebra and Its Applications, 389:159-173, 2004.
- P. Patricio, R.E. Hartwig and R. Puystjens, Diagonalizing matrices
via orthogonal Pierce decompositions, Linear Algebra and Its
Applications, 381-391, 2005.
- P. Patricio and R.E. Hartwig, On Roth's pseudo equivalence over
vol 16:111-124, 2007.
- Patricio, Pedro, Veloso da Costa, A., On the Drazin index of
regular elements, Central European Journal of Mathematics,
- Patricio, Pedro, Hartwig, R.E., Some additive results on Drazin
inverses, Applied Mathematics and Computation, 215 (2009), 530-538.
- Patricio, Pedro, Mendes Araujo, C., Moore-Penrose invertibility in
involutory rings: the case aa+=bb+, Linear and Multilinear Algebra 58(4) (2010), 445-452
- Castro-Gonzalez, N., Mendes Araujo, C., Patricio, P., "Generalized inverses of a sum in rings", Bulletin of the Australian Mathematical Society, 82 (2010), 156-164
- Patricio, P., Hartwig, R.E., "The (2,2,0) Group Inverse Problem",
Applied Mathematics and Computation 217(2) (2010), 516-520.
- Patricio, P., Hartwig, R.E., "The link between regularity and
strong-pi-regularity", Journal of the Australian Mathematical
Society 89 (2010), 17-22.
- Hartwig, R.E., Patricio, P., "When does the Moore-Penrose inverse
flip?", Operators and Matrices, 6 (1) (2012), 181-192.
- Patricio, P., "The Moore-Penrose inverse of a companion matrix",
Linear Algebra and Its Applications 437(3) (2012), 870-877.
- Hartwig, R.E., Patricio, P., "A note on power bounded matrices",
The Electronic Journal of Linear Algebra 23 (2012),
- Mary, X., Patricio, P., "The inverse along a lower triangular
matrix", Applied Mathematics and Computation 219(3) (2012),
- Patricio, P., Hartwig, R.E.; "The (2,2,0) Drazin inverse
problem", Linear Algebra and its Applications 437(11) (2012), 2755-2772
- Lebtahi, L., Patricio, P., Thome, N., "Special elements in a ring
related to Drazin inverses", Linear and
Multilinear Algebra 61(8) (2013), 1017-1027.
- Mary, X., Patricio, P., "Generalized inverses modulo H in
semigroups and rings", Linear and Multilinear Algebra 61(8) (2013), 1130-1135.
- Lebtahi, L., Patricio, P., Thome, N., "The diamond partial order in rings", Linear and Multilinear Algebra 62(3) (2014), 386-395.
- Hartwig, R.E., Patricio, P., "Two by two units", Electron. J. Linear Algebra 27 (2014), 489-503.
- Zhu, Huihui; Chen, Jianlong; Zhang, Xiaoxiang; Patricio, Pedro, "The Moore-Penrose inverse of 2x2 matrices over a certain *-regular ring". Appl. Math. Comput. 246 (2014), 263-267.
- Patricio, P., Hartwig, R.E., "Some regular sums", Linear and Multilinear Algebra, 63(1) (2015), 185-200.
- Zhu, Huihui; Chen, Jianlong; Patricio, Pedro, "Representations for the pseudo Drazin inverse of elements in a Banach algebra", Taiwanese J. Math. 19 (2015), no. 2, 349-362.
- Burgos, M.; Marquez-Garcia, M.C.; Patricio, P.; "On mappings preserving the sharp and star orders", Linear Algebra and Its Applications, 483 (2015), 268-292.
- Zhu, Huihui; Jianlong; Patricio, Pedro; Zhang, Yulin, "The inverse along a product and its applications", Linear Multilinear Algebra 64, No. 5, 834-841 (2016).
- Zhu, Huihui; Chen, Jianlong; Patricio, Pedro, "Further results on the inverse along an element in semigroups and rings", Linear Multilinear Algebra 64, No. 3, 393-403 (2016).
- Mary, Xavier; Patricio, Pedro, "The group inverse of a product", Linear and Multilinear Algebra 64, No 9, 1776-1784 (2016).
- H.H. Zhu, J.L. Chen, P. Patricio, "The Moore-Penrose inverse of differences and products of projectors in a ring with involution", Turk J Math, 40, (2016), 1316-1324.
- H.H. Zhu, J.L. Chen, P. Patricio, "Reverse order law for the inverse along an element", Linear Multilinear Algebra 65, 166-177 (2017).
- J.L. Chen, H.H. Zhu, P. Patricio, Y.L. Zhang, "Characterizations and representations of core and dual core inverses", accepted in Canad. Math. Bull.
- roland puystjens, universiteit gent, belgium
- robert e.
hartwig, ncsu, usa
- jerry koliha, university of melbourne, australia
castro-gonzalez, departamento de matematica aplicada, universidad
politecnica de madrid
- claudia mendes araujo, universidade do minho
- antonio veloso da costa, universidade do minho
- xavier mary, universite' paris-ouest
- nestor thome', universitat politecnica de valencia
- leila lebtahi, universitat politecnica de valencia
- huihui zhu, (PhD student, co-supervised with Jianlong Chen), southeast university, nanjing, pr china
- honglin zou, (visiting PhD student), southeast university, nanjing, pr china
member of the centro de
matematica - cmat, SPM and ILAS
my Erdos numer is 4.
the Erdos number of a person is the length of a shortest chain of joint
mathematical publications leading to the famous mathematician Paul Erdos
(see all about that here). My
(Rodl, Muller), (Muller, Koliha),
P. Erdos and V.
Rodl, Coverings of r-graphs by complete r-partite subgraphs, Random
Structures Algorithms 6 (1995), 2-3.
V. Muller and
V. Rodl, Monotone paths in ordered graphs, Combinatorica
2 (1982), 193-201.
J. J. Koliha,
M. Mbekhta, V. Muller and P. W. Poon, Corigendum and addendum:
"On the axiomatic theory of the spectrum II", Studia
Mathematica 130 (1998), 193-198.
another path (from the mathscinet):
Pedro Patricio coauthored with Robert E. Hartwig
Robert E. Hartwig coauthored with Frank J. Hall
MR0404288 (53 #8090)
Frank J. Hall coauthored with Guantao Chen MR1821633
Guantao Chen coauthored with Paul Erdos MR1215330
Bulletin of the Belgium Math. Soc. - Simon Stevin
Central European Journal of Mathematics
Journal of the Australian Mathematical Society
Linear Algebra and Its Applications
Soochow Journal of Mathematics
i am interested by everything concerning hi-fi, but i am far from being
an audiophile. in any case, i have as an universal digital source a
denon 2900 (super-audio CD, DVD-audio) and a denon 3803 as a receiver.
visonik was the choice for
loudspeakers: two pairs of evolution 6 for front+surround and one
evolution center as central channel. interconnects include nordost, qed
an important source of reviews and news is the home cinema choice site,
with lots of tests and comparisons. discussion foruns i try to follow
include dvdmania, forum hi-fi, avforum, avforums. PT source of news and
NOTICE: this is quite old; i'll update it whenever i find the time and mood :-)
i have been using linux since 2000. i have used mandrake (now mandriva)
and suse (which i really recommed, namely the 10.0). at home i have and
old compaq armada E700 laptop (more like a brick, nowadays), with a
pentium II @ astonishing ;-) 400MHz, together with 128Mb ram and 20G
hard drive. it drags quite a bit, and some patience is required. it is
running mepis, a former debian based
distro, and since 2006 a ubuntu based distro (screenshot here). at my office, i was fortunate enough
to receive a 3.0GHz dual core pentium, with 512Mb ram. after using
mepis, i experienced and was delighted to use kororaa, a gentoo based distro, with XGL support
(see screenshots here and here). i have, in october '06, upgraded to
Kororaa AIGLXgl (v 0.3), running on AIXGL (screenshot here and here).
in the labs i use fedora-core, and centOS in our server (where this page
preferred software: the firefox family, kile+latex,
octave/pari-gp/mupad, emacs, vi ;-) and kwrite, gimp (!), openoffice for
received (M$)office documents.
info on this subject can be found at /., and it's portuguese version gildot. i also check for news and
discussions in the spanish barrapunto and in the brazilian vivaolinux. i keep track on the
distro's update by checking (RSS feeds!!!) distrowatch.com, osnews.com and desktoplinux.com.