منابع مشابه
The Norm Dependence of Singular Vectors
For a linearized system such as ]c/]t 5 Mc, singular vector analysis can be used to find patterns that give the largest or smallest ratios between the sizes of Mc and c. Such analyses have applications to a wide range of atmosphere–ocean problems. The resulting singular vectors, however, depend on the norm used to measure the sizes of Mc and c, as noted in various applications. This causes comp...
متن کاملBases of minimal vectors in lattices, II
We prove that a Euclidean lattice of dimension n = 5 (resp. 6; resp. 7) having at least 6 (resp. 10; resp. 18) pairs of minimal vectors has a basis of minimal vectors. Résumé. Nous montrons qu’un réseau euclidien de dimension n = 5 (resp. 6; resp. 7) ayant au moins 6 (resp. 10; resp. 18) paires de vecteurs minimaux possède une base de vecteurs minimaux. Titre français : Bases de vecteurs minima...
متن کاملOrthogonalization of Vectors with Minimal Adjustment
A new transformation is proposed that gives orthogonal components with a one-to-one correspondence between the original vectors and the components. The aim is that each component should be close to the vector with which it is paired, orthogonality imposing a constraint. If the vectors have been normalized, then the transformation minimizes the sum of the squared correlations between each vector...
متن کاملBases of minimal vectors in lattices, I
We prove that a Euclidean lattice of dimension n ≤ 8 which is generated by its minimal vectors possesses a basis of minimal vectors. Résumé. Nous montrons qu’un réseau euclidien de dimension n ≤ 8 engendré par ses vecteurs minimaux possède une base de vecteurs minimaux. Titre français : Bases de vecteurs minimaux dans les réseaux, I. Mathematics Subject Classification (2000). 11H55.
متن کاملAsymptotics of the norm of elliptical random vectors
In this paper we consider elliptical random vectors X in IR, d ≥ 2 with stochastic representation ARU , where R is a positive random radius independent of the random vector U which is uniformly distributed on the unit sphere ofIR and A ∈IRd×d is a given matrix. Denote by ‖·‖ the Euclidean norm inIR, and let F be the distribution function of R with upper endpoint xF . The main result of this pap...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-04703-0