51,408 research outputs found
Characterizations of k-commutative equalities for some outer generalized inverses
[EN] In this paper, we present necessary and sufficient conditions for the k-commutative equality , where X is an outer generalized inverse of the square matrix A. Also, we give new representations for core EP, DMP, and CMP inverses of square matrices as outer inverses with prescribed null space and range. In addition, we characterize the core EP inverse as the solution of a new system of matrix equations.D. E. Ferreyra F. E. Levis Partially supported by a Consejo Nacional de Investigaciones Científicas y Técnicas CONICET s Posdoctoral Research Fellowship, UNRC [grant number PPI 18/C472] and CONICET
[grant number PIP 112-201501-00433CO], respectively. N. Thome Partially supported by Secretaría de Estado de Investigación, Desarrollo e Innovación Ministerio de Economía, Industria y Competitividad of Spain [grant number DGI MTM2013-43678-P and Grant Red de Excelen- cia PMTM2017-90682-REDT]. D. E. Ferreyra and N. Thome Partially supported Universidad Nacional de La Pampa (UNLPam), Facultad de Ingeniería [grant Resol. No 155/14].Ferreyra, DE.; Levis, F.; Thome, N. (2018). Characterizations of k-commutative equalities for some outer generalized inverses. Linear and Multilinear Algebra. 1-16. https://doi.org/10.1080/03081087.2018.1500994S116Baksalary, O. M., & Trenkler, G. (2010). Core inverse of matrices. Linear and Multilinear Algebra, 58(6), 681-697. doi:10.1080/03081080902778222Manjunatha Prasad, K., & Mohana, K. S. (2013). Core–EP inverse. Linear and Multilinear Algebra, 62(6), 792-802. doi:10.1080/03081087.2013.791690Malik, S. B., & Thome, N. (2014). On a new generalized inverse for matrices of an arbitrary index. Applied Mathematics and Computation, 226, 575-580. doi:10.1016/j.amc.2013.10.060Mehdipour, M., & Salemi, A. (2017). On a new generalized inverse of matrices. Linear and Multilinear Algebra, 66(5), 1046-1053. doi:10.1080/03081087.2017.1336200Malik, S. B., Rueda, L., & Thome, N. (2016). The class ofm-EPandm-normal matrices. Linear and Multilinear Algebra, 64(11), 2119-2132. doi:10.1080/03081087.2016.1139037Wang, H. (2016). Core-EP decomposition and its applications. Linear Algebra and its Applications, 508, 289-300. doi:10.1016/j.laa.2016.08.008Wang H, Chen J. Weak group inverse. Available from: http://arxiv.org/abs/1704.08403v1Wei, Y. (1998). A characterization and representation of the generalized inverse A(2)T,S and its applications. Linear Algebra and its Applications, 280(2-3), 87-96. doi:10.1016/s0024-3795(98)00008-1Rakić, D. S., Dinčić, N. Č., & Djordjević, D. S. (2014). Core inverse and core partial order of Hilbert space operators. Applied Mathematics and Computation, 244, 283-302. doi:10.1016/j.amc.2014.06.112Stanimirović, P. S., Katsikis, V. N., & Ma, H. (2016). Representations and properties of theW-Weighted Drazin inverse. Linear and Multilinear Algebra, 65(6), 1080-1096. doi:10.1080/03081087.2016.1228810Ferreyra, D. E., Levis, F. E., & Thome, N. (2017). Revisiting the core EP inverse and its extension to rectangular matrices. Quaestiones Mathematicae, 41(2), 265-281. doi:10.2989/16073606.2017.1377779Deng, C. Y., & Du, H. K. (2009). REPRESENTATIONS OF THE MOORE-PENROSE INVERSE OF 2×2 BLOCK OPERATOR VALUED MATRICES. Journal of the Korean Mathematical Society, 46(6), 1139-1150. doi:10.4134/jkms.2009.46.6.1139Wang, H., & Liu, X. (2014). Characterizations of the core inverse and the core partial ordering. Linear and Multilinear Algebra, 63(9), 1829-1836. doi:10.1080/03081087.2014.97570
Representations for generalized Drazin inverse of operator matrices over a Banach space
In this paper we give expressions for the generalized Drazin inverse of a
(2,2,0) operator matrix and a operator matrix under certain
circumstances, which generalizes and unifies several results in the literature
Classification of Matrix Product States with a Local (Gauge) Symmetry
Matrix Product States (MPS) are a particular type of one dimensional tensor
network states, that have been applied to the study of numerous quantum many
body problems. One of their key features is the possibility to describe and
encode symmetries on the level of a single building block (tensor), and hence
they provide a natural playground for the study of symmetric systems. In
particular, recent works have proposed to use MPS (and higher dimensional
tensor networks) for the study of systems with local symmetry that appear in
the context of gauge theories. In this work we classify MPS which exhibit local
invariance under arbitrary gauge groups. We study the respective tensors and
their structure, revealing known constructions that follow known gauging
procedures, as well as different, other types of possible gauge invariant
states
Non-universal Z' from SO(10) GUTs with vector-like family and the origin of neutrino masses
A gauge boson with mass around the (few) TeV scale is a popular example
of physics beyond the Standard Model (SM) and can be a fascinating remnant of a
Grand Unified Theory (GUT). Recently, models with non-universal couplings
to the SM fermions due to extra vector-like states have received attention as
potential explanations of the present , anomalies; this
includes GUT model proposals based on the group. In this
paper we further develop GUT models with a flavour non-universal low scale
and clarify several outstanding issues within them. First, we successfully
incorporate a realistic neutrino sector (with linear and/or inverse low scale
seesaw mechanism), which was so far a missing ingredient. Second, we
investigate in detail their compatibility with the ,
anomalies; we find that the anomalies do not have a consistent explanation
within such models. Third, we demonstrate that these models have other
compelling phenomenological features; we study the correlations between the
flavour violating processes of and - conversion in a muonic
atom, showing how a GUT imprint could manifest itself in experiments.Comment: Revised version, published in NPB. New material, general conclusions
unchanged. 30 pages, 4 figures, 2 table
Fast Fourier Transforms for the Rook Monoid
We define the notion of the Fourier transform for the rook monoid (also
called the symmetric inverse semigroup) and provide two efficient
divide-and-conquer algorithms (fast Fourier transforms, or FFTs) for computing
it. This paper marks the first extension of group FFTs to non-group semigroups
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