71 documents found, page 1 of 8
When is a product of EP elements again EP?
Mary, Xavier; Patrício, PedroIn this paper, we give necessary and sufficient conditions for a product of EP elements to be EP, in Dedekind-finite ∗-rings. The proofs rely on descriptions of Morita contexts (via Peirce matrix forms) as corner rings of 2x2 matrix rings.
Generalized inverses of special matrices partitioned into blocks
Almeida, Regina de; Catarino, Paula; Patrício, Pedro; Vicente, M. A. Facas; Vitória, JoséIt is known the connection between the best approximation and Moore-Penrose invertibility. In particular, the best approximation pair of two affine subspaces is related to generalized invertibility of a block matrix of the form $\left[\begin{array}{cc} I_n & A\\ B & I_m\end{array}\right]$. In this paper, we address the Moore-Penrose inverse and the group inverse of a block matrix $\left[\begin{array}{cc} I_n & ...
On generalized inverses of matrices associated with certain graph classes
Araújo, C. Mendes; Patrício, Pedro; Maciala, Faustino AntónioWe investigate generalized inverses of matrices associated with two classes of digraphs: double star digraphs and D-linked stars digraphs. For double star digraphs, we determine the Drazin index and derive explicit formulas for the Drazin inverse. We also provide necessary and sufficient conditions for the ex istence of the Moore–Penrose inverse and give its explicit expression whenever it exists. For D-linked ...
Deliberate self-harm in adolescence: a cross-sectional study
Mendes, Joana; Vieira Martins, Miguel; Azevedo, Isabel; Patrício, Pedro; Ferreira, SofiaIntroduction: The high prevalence of deliberate self-harm (DSH) and its strong association with suicide make the condition a natural target for intervention to prevent harmful consequences for adolescents. The aim of this study was to determine the prevalence of DSH and to characterize DSH patterns and associated risk factors in a sample of adolescents. Methods: A cross-sectional study was conducted by applying...
The (B,C)-core inverse of rectangular matrices
Zhu, Huihui; Xu, Daihan; Patrício, Pedro; Mosić, DijanaLet A be an m × n complex matrix and let B, C be n × m complex matrices. The main purpose of this article is to derive several new properties of the (B, C)-core inverse. Also, we introduce and investigate the dual (B, C)-core inverse in the context of rectangular matrices. The connection between (dual) (B, C)-core inverses and other generalized inverses is given. Finally, the minimum norm solution and least squ...
Deliberate self-harm in adolescence: a cross-sectional study
Mendes, Joana; Martins, Miguel Vieira; Azevedo, Isabel; Patrício, Pedro; Ferreira, SofiaIntroduction: The high prevalence of deliberate self-harm (DSH) and its strong association with suicide make the condition a natural target for intervention to prevent harmful consequences for adolescents. The aim of this study was to determine the prevalence of DSH and to characterize DSH patterns and associated risk factors in a sample of adolescents. Methods: A cross-sectional study was conducted by applying...
Divisibility of finite geometric series
Hartwig, Robert E.; Patrício, PedroWe give necessary and sufficient conditions for the divisibility of two finite geometric series $G_n(x)=1+x+x^2+···+x^{n−1}$ over a field of characteristic zero.
Characterizations and representations of left and right hybrid (b, c)-inverses ...
Zhu, Huihui; Wu, Liyun; Peng, Fei; Patrício, PedroLet R be an associative ring with unity 1 and let a, b ,c is an element of R. In this paper, several characterizations for left and right hybrid (b, c)-inverses of a are derived. Moreover, their formulae are given by regularities of certain elements. Then, we give characterizations of right (b, c)-inverses and right annihilator (b, c)-inverses of the product of three elements. Finally, relations among the right...
Continuity of the core-EP inverse and its applications
Gao, Yuefeng; Chen, Jianlong; Patrício, PedroIn this paper, firstly we study the continuity of the core-EP inverse without explicit error bounds by virtue of two methods. One is the rank equality, followed from the classical generalized inverse. The other one is matrix decomposition. The continuity of the core inverse can be derived as a particular case. Secondly, we study perturbation bounds for the core-EP inverse under prescribed conditions. Perturbati...
From euclid to corner sums - a trail of telescoping tricks
Patrício, Pedro; Hartwig, Robert E.Euclid's algorithm is extended to binomials, geometric sums and corner sums. Two-sided non-commuting, non-constant linear difference equations will be solved, and the solution is applied to corner sums, thereby presenting an explicit formula for the generator of the bi-module spanned by the two starting corner sums.