منابع مشابه
Joint mixability of some integer matrices
We study the problem of permuting each column of a given matrix to achieve minimum maximal row sum or maximum minimal row sum, a problem of interest in probability theory and quantitative finance where quantiles of a random variable expressed as the sum of several random variables with unknown dependence structure are estimated. If the minimum maximal row sum is equal to the maximum minimal row...
متن کاملLectures on Integer Matrices
Introduction 2 Lecture 1. Hermite and Smith normal forms 3 Lecture 2. Integral similarity and the Latimer-MacDuffee-Taussky theorem 8 Lecture 3. Ideal class numbers, integral matrices nonderogatory modulo every prime and maximal orders of number fields 12 Lecture 4. Factorizations of integer matrices as products of elementary matrices, involutions etc 20 Lecture 5. Additive commutators. Solving...
متن کاملSome Elimination Problems for Matrices
problem: Given: A field K and n variables x1, . . . , xn and m polynomials yi = pi(x1, . . . , xn) ∈ K[x1, . . . , xn] for i = 1, . . . ,m. (1) Aim: Find a presentation for the subring K[y] := K[y1, . . . , ym] of K[x] := K[x1, . . . , xn]. Invariants: The difference of m and the transcendence degree of K(y) := K(y1, . . . , ym) over K will be called the deficiency d = d(y) of the tuple y in K(...
متن کاملSome decision problems
Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free, 2) contains the identity matrix, 3) contains the null matrix or 4) is a group. Even for matrices of dimension 3, questions 1) and 3) are undecidable. For dimension 2, they are still open as far as we know. Here we prove that problems 2) and 4) are decidable ...
متن کاملOn the WZ Factorization of the Real and Integer Matrices
The textit{QIF} (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ} factorization. The WZ factorization can be faster than the textit{LU} factorization because, it performs the simultaneous evaluation of two columns or two rows. Here, we present a method for computing the real and integer textit{WZ} and textit{ZW} factoriz...
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ژورنال
عنوان ژورنال: RAIRO - Theoretical Informatics and Applications
سال: 2005
ISSN: 0988-3754,1290-385X
DOI: 10.1051/ita:2005007