Results 31 to 40 of about 622,326 (127)
Toeplitz matrices with totally nonnegative inverses
Linear Algebra and its Applications, 1979 AbstractIt is shown that the inverse of a Toeplitz matrix has only nonnegative minors if the zeros of a certain polynomial are positive or if their arguments are less than π⧸(k+n), where n is the dimension and k+1 is the bandwidth of the matrix.
Lorenz, Jens, Mackens, Wolfgang
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Totally nonnegative cells and Matrix Poisson varieties [PDF]
, 2011 We describe explicitly the admissible families of minors for the totally nonnegative cells of real matrices, that is, the families of minors that produce nonempty cells in the cell decompositions of spaces of totally nonnegative matrices introduced by A.
Lenagan, T.H. +9 more
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Three observations on nonnegative matrices
, 1967 Some results on nonnegative matrices are proved, of which the following is representative: Let A = (aij) be a nonnegative row stochastic matrix. If [formula not included] is an eigenvalue of A, then [equation]
Hoffman, A. J.
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Barrett-Johnson inequalities for totally nonnegative matrices
, 2022 Given a matrix $A$, let $A_{I,J}$ denote the submatrix of $A$ determined by rows $I$ and columns $J$. Fischer's Inequalities state that for each $n \times n$ Hermitian positive semidefinite matrix $A$, and each subset $I$ of $\{1,\dotsc,n\}$ and its complement $I^c$, we have $\det(A) \leq \det(A_{I,I})\det(A_{I^c,I^c})$.
Skandera, Mark, Soskin, Daniel
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Intervals of almost totally positive matrices [PDF]
, 2003 We consider the class of the totally nonnegative matrices, i.e., the matrices having all their minors nonnegative, and intervals of matrices with respect to the chequerboard partial ordering, which results from the usual entrywise partial ordering if we ...
Garloff, Jürgen
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Nonnegative square roots of nonnegative matrices
, 2014 By a square root of a (square) matrix A we mean a matrix B that satisfies B2 = A. The study of square roots or pth roots of a general (real or complex) matrix can be traced back to the early work of Cayley [1], [2], Sylvester [11], Frobenius [6] in the ...
譚必信
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The Sinkhorn-Knopp algorithm : convergence and applications [PDF]
, 2008 As long as a square nonnegative matrix A contains sufficient nonzero elements, then the Sinkhorn-Knopp algorithm can be used to balance the matrix, that is, to find a diagonal scaling of A that is doubly stochastic.
Knight, P.A.
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On the geometric interpretation of the nonnegative rank [PDF]
The nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank-one factors needed to reconstruct it exactly. The problem of determining this rank and computing the corresponding nonnegative factors is difficult; however it has ...
GILLIS, Nicolas, GLINEUR, François
core
Hadamard powers and totally positive matrices [PDF]
, 2007 Considered are continuous, positive Hadamard powers of entry-wise positive (nonnegative) matrices. Those that are eventually (in the sense of all Hadamard powers beyond some point) totally positive, totally nonnegative, doubly nonnegative and doubly ...
Fallat, Shaun M., Johnson, Charles R.
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Totally positive matrices and totally positive hypergraphs [PDF]
, 2001 A real matrix is totally positive if all its minors are nonnegative. In this paper, we characterize 0–1 matrices that can be transformed into totally positive matrices by permutations of rows and ...
Lehel, Jenő +2 more
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