On generators of bounded ratios of minors for totally positive matrices
نویسندگان
چکیده
منابع مشابه
On generators of bounded ratios of minors for totally positive matrices
We provide a method for factoring all bounded ratios of the form det A(I1|I ′ 1) det A(I2|I ′ 2)/ det A(J1|J ′ 1) det A(J2|J ′ 2) where A is a totally positive matrix, into a product of more elementary ratios each of which is bounded by 1, thus giving a new proof of Skandera’s result. The approach we use generalizes the one employed by Fallat et al. in their work on principal minors. We also ob...
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.
متن کاملBounded Ratios of Products of Principal Minors of Positive Definite Matrices
Considered is the multiplicative semigroup of ratios of products of principal minors bounded over all positive definite matrices. A long history of literature identifies various elements of this semigroup, all of which lie in a subsemigroup generated by Hadamard-Fischer inequalities. Via cone-theoretic techniques and the patterns of nullity among positive semidefinite matrices, a semigroup cont...
متن کاملArrangements and Amounts of Equal Minors in Totally Positive Matrices
Understanding the positive Grassmannian has been a highly significant question in mathematics for several decades. We discuss arrangements of equal minors in the totally positive Grassmannian. It was previously shown that arrangements of equals minors of largest value correspond to the simplices in Sturmfels triangulation. Here we discuss arrangements of equals minors of second largest value, a...
متن کاملOn Factorizations of Totally Positive Matrices
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. Conditions of uniqueness for the decomposition are also given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.10.011