vol16_pp162-170. 116KB Jun 04 2011 12:05:57 AM
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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
This paper extends the Nilpotent- Jacobian method for sign pattern matrices to complex sign pattern matrices, establishing a means to show that an irreducible complex sign
Matrix functions, Generalization of nonnegative matrices, Eventually nonnegative matrices, Eventually positive matrices, Exponentially nonnegative matrices, Eventually exponen-
For such matrices this improves on a bound found in the work of Doerr [Linear discrepancy of basic totally unimodular matrices, The Electronic Journal of Combinatorics, 7:Research
Nonnegative matrices, Diagonal similarity scaling, Diagonal equivalence scaling, Digraph of a matrix, Cyclic product, Cycle mean, Lattice ordered commutative groups.. AMS
Another collection of potentially nilpotent but not spectrally arbitrary sign patterns can be obtained by following an argument of [4] and noting that any reducible sign pattern
In the context of invertible M-matrices (i.e., when B ≥ 0), condition (ii) of Theorem 4.3 is associated with diagonal dominance of AD because the diagonal entries are positive and
For example, in [3], it is shown that a positive semigroup whose diagonal entries are binary (equal to 0 or 1), is either decomposable, or similar, via a positive diagonal
