منابع مشابه
The Tropical Totally Positive Grassmannian
Tropical algebraic geometry is the geometry of the tropical semiring (R,min,+). The theory of total positivity is a natural generalization of the study of matrices with all minors positive. In this paper we introduce the totally positive part of the tropicalization of an arbitrary affine variety, an object which has the structure of a polyhedral fan. We then investigate the case of the Grassman...
متن کاملImmanants of Totally Positive Matrices Are Nonnegative
If/ is an irreducible character of Sn, these functions are known as immanants; if/ is an irreducible character of some subgroup G of Sn (extended trivially to all of Sn by defining /(vv) = 0 for w$G), these are known as generalized matrix functions. Note that the determinant and permanent are obtained by choosing / to be the sign character and trivial character of Sn, respectively. We should po...
متن کاملTotally Positive Density Matrices and Linear Preservers
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. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Hig...
متن کاملOn totally positive matrices and geometric incidences
Article history: Received 3 September 2013 Available online xxxx
متن کاملEla Zero Minors of Totally Positive Matrices
In this paper the structure of the zero minors of totally positive matrices is studied and applications are presented.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2018
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2018.07.005