1. Improved tests and characterizations of totally nonnegative matrices
- Author
-
Mohammad Adm and Juergen Garloff
- Subjects
Discrete mathematics ,Algebra and Number Theory ,Totally nonnegative matix, totally positive matrix, Cauchon algorithm, Neville elimination, bidiagonalization ,Neville elimination ,Mathematical proof ,law.invention ,Combinatorics ,Set (abstract data type) ,Invertible matrix ,Bidiagonalization ,law ,msc:15A48 ,Totally positive matrix ,Nonnegative matrix ,ddc:510 ,Connection (algebraic framework) ,Mathematics - Abstract
Totally nonnegative matrices, i.e., matrices having all minors nonnegative, are con- sidered. A condensed form of the Cauchon algorithm which has been proposed for finding a param- eterization of the set of these matrices with a fixed pattern of vanishing minors is derived. The close connection of this variant to Neville elimination and bidiagonalization is shown and new determi- nantal tests for total nonnegativity are developed which require much fewer minors to be checked than for the tests known so far. New characterizations of some subclasses of the totally nonnegative matrices as well as shorter proofs for some classes of matrices for being (nonsingular and) totally nonnegative are derived.
- Published
- 2014
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