Results 11 to 20 of about 10,628 (259)
Totally positive matrices and totally positive hypergraphs
Linear Algebra and its Applications, 2001 This paper characterizes (0,1)-matrices which are totally positive, that is, all their minors are totally positive. First the case of \(1\times 1\) and \(2\times 2\) minors is characterized in terms of interval hypergraphs and then the general case is characterized in terms of a chain of cliques \(C_i\), \(C_i\cap C_j = \emptyset \Leftrightarrow |i-j ...
Kubicki, Grzegorz +2 more
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Tropical totally positive matrices [PDF]
Journal of Algebra, 2018 The first author has been partially supported by the PGMO Program of FMJH and EDF, and by the MALTHY Project of the ANR Program.
Gaubert, Stéphane, Niv, Adi
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Matrices totally positive relative to a tree [PDF]
The Electronic Journal of Linear Algebra, 2009 It is known that for a totally positive (TP) matrix, the eigenvalues are positive and distinct and the eigenvector associated with the smallest eigenvalue is totally nonzero and has an alternating sign pattern. Here, a certain weakening of the TP hypothesis is shown to yield a similar conclusion.
Jhondon, Charles R. +2 more
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Generalized totally positive matrices
Linear Algebra and its Applications, 2000 A matrix over a ring with identity and a positive part is called generalized totally positive (GTP) if the Schur complements are positive in all nested sequences of so-called relevant submatrices, i.e. ones having either the first \(k\) rows and \(k\) consecutive columns, or \(k\) consecutive rows and the first \(k\) columns.
Fiedler, Miroslav, Markham, Thomas L.
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On Factorizations of Totally Positive Matrices [PDF]
, 1996 Different approaches to the decomposition of a nonsingular totally positive matrix as a product of bidiagonal matrices are studied. Special attention is paid to the interpretation of the factorization in terms of the Neville elimination process of the matrix and in terms of corner cutting algorithms of Computer Aided Geometric Design.
Mariano Gasca, Juan M. Peña
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Intervals of almost totally positive matrices
Linear Algebra and its Applications, 2003 The author shows that a stronger form of the total nonnegativity is preserved on matrix intervals with respect to the chequerboard partial ordering on the real nonsingular matrices. The analogous question for totally nonnegative matrices seems to remain open since 1996.
Garloff, Jürgen
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Inner totally positive matrices
Linear Algebra and its Applications, 2004 The author considers the concept of inner total positivity. In Section 1, he describes the notation and basic theory used in this paper, concerning totally positivity and nonnegativity. In Section 2, he generalizes the results in Section 1 to inner totally positive (totally nonnegative) matrices.
Gladwell, G.M.L.
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Matrices totally positive relative to a tree, II [PDF]
Linear Algebra and its Applications, 2016 In this paper we prove that for a general tree $T$, if $A$ is T-TP, all the submatrices of $A$ associated with the deletion of pendant vertices are $P$-matrices, and $\det A>0$, then the smallest eigenvalue has an eigenvector signed according to $T$.
R.S. Costas-Santos, C.R. Johnson
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Totally Positive Density Matrices and Linear Preservers
The Electronic Journal of Linear Algebra, 2016 The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated.
Kribs, David W. +2 more
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Totally positive matrices and cyclic polytopes
Linear Algebra and its Applications, 1988 As the main result of the present note it is proved that there is a natural correspondence between alternating polytopes and totally positive matrices. A real (n-d)\(\times d\) matrix A, where \(n>d>1\) is totally positive (totally nonnegative) if all subdeterminants of A are positive (nonnegative).
Sturmfels, Bernd, Sturmfels, B.
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