Perron–Frobenius theorem for nonnegative multilinear forms and extensions
نویسندگان
چکیده
منابع مشابه
Multilinear forms which are products of linear forms
The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.
متن کاملMultilinear forms
Proposition 1.1. α1, . . . , αn forms a basis for V ∗ (called the dual basis). In particular, this shows that V and V ∗ are vector spaces of the same dimension. However, there is no natural way to choose an isomorphism between them, unless we pick some additional structure on V (such as a basis or a nondegenerate bilinear form). On the other hand, we can construct an isomorphism ψ from V to (V ...
متن کاملCongruence of Multilinear Forms
Let F : U × · · · × U → K, G : V × · · · × V → K be two n-linear forms with n > 2 on vector spaces U and V over a field K. We say that F and G are symmetrically equivalent if there exist linear bijections φ1, . . . , φn : U → V such that F (u1, . . . , un) = G(φi1u1, . . . , φinun) for all u1, . . . , un ∈ U and each reordering i1, . . . , in of 1, . . . , n. The forms are said to be congruent ...
متن کاملMultilinear perceptron convergence theorem.
An adaptive perceptron with multilinear couplings is introduced. While an adap-tive perceptron exhibits severe shortcomings if it is applied to complex tasks, this is not so for the adaptive multilinear perceptron.
متن کاملCramer's Theorem for Nonnegative Summands
We clarify the boundary effect in Cramer’s theorem on the Large Deviations Principle (LDP) for normed sums of non-negative i.i.d. random variables Sn = 1 n ∑ n i=1 ξi. We show that the LDP holds true with the rate function possibly infinite at the boundary point x = 0. We also consider a continuous time version of Cramer’s theorem with nonnegative summands St = 1 t ∑ i:τi≤t ξi, t → ∞, where (τi...
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: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.02.042