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Some results on B-matrices and doubly B-matrices
Ara??jo, C. Mendes; Torregrosa, Juan R.A real matrix with positive row sums and all its off-diagonal elements bounded above by their corresponding row means was called in [4] a B-matrix. In [5], the class of doubly B-matrices was introduced as a generalization of the previous class. We present several characterizations and properties of these matrices and for the class of B-matrices we consider corresponding questions for subdirect sums of two matri...
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.
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...
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...
The N-matrix completion problem under digraphs assumptions
Araújo, C. Mendes; Torregrosa, Juan R.; Urbano, Ana M.An $n \times n$ matrix is called an $N$--matrix if all principal minors are negative. In this paper, we are interested in the partial $N$--matrix completion problem, when the partial $N$--matrix is non-combinatorially symmetric. In general, this type of partial matrices does not have an $N$--matrix completion. We prove that a non-combinatorially symmetric partial $N$--matrix has an $N$--matrix completion if the...
N-matrix completion problem
Araújo, C. Mendes; Torregrosa, Juan R.; Urbano, Ana M.An n x n matrix is called an N-matrix if all principal minors are negative. In this paper, we are interested in N-matrix completion problems, that is, when a partial N-matrix hás an N-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial N-matrix does not have an N-matrix completion. Here we prove that a combinatorially symmetric partial N-matrix has an N-matrix completion if...
The completion problem for N-matrices
Araújo, C. Mendes; Torregrosa, Juan R.An $n\times m$ matrix is called an $N$-matrix if all principal minors are negative. In this paper, we are interested in $N$-matrix completion problems, that is, when a partial $N$-matrix has an $N$-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial $N$-matrix does not have an $N$-matrix completion. Here, we prove that a combinatorially symmetric partial $N$-matrix has an $...
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