Encontrados 14 documentos, a visualizar página 1 de 2
Raciocínios desenvolvidos na verificação das soluções de sistemas de equações l...
Barros, Paula Maria; Fernandes, José António; Araújo, C. MendesNuma investigação sobre o ensino e aprendizagem de álgebra Linear, em que um dos objetivos era identificar os erros e dificuldades sentidos pelos estudantes, propuseram-se algumas questões sobre sistemas de equações lineares a estudantes de engenharia do ensino superior politécnico que frequentavam a unidade curricular álgebra linear e geometria analítica. Neste texto, faz-se uma breve exposição dos resultados ...
Sign pattern matrices that admit P_0-matrices
Araújo, C. Mendes; Torregrosa, Juan R.For sign patterns corresponding to directed or undirected cycles, we identify conditions under which the patterns admit or require P0–matrices.
Moore-Penrose invertibility in involutory rings : the case aa+=bb+
Patrício, Pedro; Araújo, C. MendesIn this article, we consider Moore-Penrose invertibility in rings with a general involution. Given two von Neumann regular elements a, b in a general ring with an arbitrary involution, we aim to give necessary and sufficient conditions to aa† = bb†. As a special case, EP elements are considered.
Generalized inverses of a sum in rings
Castro-González, N.; Araújo, C. Mendes; Patrício, PedroDocumento submetido para revisão pelos pares. A publicar em "Bulletin of the Australian Mathematical Society". ISSN 0004-9727. 82:1 (2010) 156-164. ; We study properties of the Drazin index of regular elements in a ring with a unity 1. We give expressions for generalized inverses of 1 − ba in terms of generalized inverses of 1 − ab. In our development we prove that the Drazin index of 1 − ba is equal to the Dr...
N_0 completions on partial matrices
Araújo, C. Mendes; Torregrosa, Juan R.; Jordán, CristinaAn $n\times n$ matrix is called an $N_0$-matrix if all its principal minors are nonpositive. In this paper, we are interested in $N_0$-matrix completion problems, that is, when a partial $N_0$-matrix has an $N_0$-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial $N_0$-matrix does not have an $N_0$-matrix completion. Here, we prove that a combinatorially symmetric partial ...
Sign pattern matrices that admit M-, N-, P- or inverse M-matrices
Araújo, C. Mendes; Torregrosa, Juan R.In this paper we identify the sign pattern matrices that occur among the N–matrices, the P–matrices and the M–matrices. We also address to the class of inverse M–matrices and the related admissibility of sign pattern matrices problem.
Totally nonpositive completions on partial matrices
Araújo, C. Mendes; Torregrosa, Juan R.; Urbano, Ana M.An n £ n real matrix is said to be totally no positive if every minor is no positive. In this paper, we are interested in totally no positive completion problems, that is, does A partial totally no positive matrix have a totally no positive matrix completion? This Problem has, in general, a negative answer. Therefore, we analyze the question: for which Labelled graphs G does every partial totally no positive ma...
Actas do Encontro de Algebristas Portugueses 2005
Araújo, C. Mendes; Gonçalves, Suzana Mendes; Martins, Paula Mendes; Patrício, PedroOs 16 artigos que constituem este livro de actas baseiam-se em comunicações apresentadas no Encontro de Algebristas Portugueses 2005 - EAP2005. O EAP2005 realizou-se de 22 a 24 de Setembro, nas instalações da Escola de Ciências da Universidade do Minho, e contou com 49 participantes, vindos de vários pontos do país. O principal objectivo deste encontro foi fomentar o intercâmbio científico entre os membros de u...
The symmetric N-matrix completion problem
Araújo, C. Mendes; Torregrosa, Juan R.; Urbano, Ana M.An $n\times n$ matrix is called an $N$-matrix if all its principal minors are negative. In this paper, we are interested in the symmetric $N$-matrix completion problem, that is, when a partial symmetric $N$-matrix has a symmetric $N$-matrix completion. Here, we prove that a partial symmetric $N$-matrix has a symmetric $N$-matrix completion if the graph of its specified entries is chordal. Furthermore, if this g...
The doubly negative matrix completion problem
Araújo, C. Mendes; Torregrosa, Juan R.; Urbano, Ana M.An $n\times n$ matrix over the field of real numbers is a doubly negative matrix if it is symmetric, negative definite and entry-wise negative. In this paper, we are interested in the doubly negative matrix completion problem, that is when does a partial matrix have a doubly negative matrix completion. In general, we cannot guarantee the existence of such a completion. In this paper, we prove that every partial...
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