منابع مشابه
On Maximum, Typical, and Generic Ranks
We show that for several notions of rank including tensor rank, Waring rank, and generalized rank with respect to a projective variety, the maximum value of rank is at most twice the generic rank. We show that over the real numbers, the maximum value of the real rank is at most twice the smallest typical rank, which is equal to the (complex) generic rank.
متن کاملGeneric and Typical Ranks of Multi-Way Arrays
The concept of tensor rank was introduced in the twenties. In the seventies, when methods of Component Analysis on arrays with more than two indices became popular, tensor rank became a much studied topic. The generic rank may be seen as an upper bound to the number of factors that are needed to construct a random tensor. We explain in this paper how to obtain numerically in the complex field t...
متن کاملOn Higher Real and Stable Ranks for CCR C−algebras
We calculate the real rank and stable rank of CCR algebras which either have only finite dimensional irreducible representations or have finite topological dimension. We show that either rank of A is determined in a good way by the ranks of an ideal I and the quotient A/I in four cases: When A is CCR; when I has only finite dimensional irreducible representations; when I is separable, of genera...
متن کاملOn the typical rank of real binary forms
We determine the rank of a general real binary form of degree d = 4 and d = 5. In the case d = 5, the possible values of the rank of such general forms are 3, 4, 5. The existence of three typical ranks was unexpected. We prove that a real binary form of degree d with d real roots has rank d.
متن کاملOn the Typical Rank of Real Closed Fields
In this note we introduce the notion of typical rank for any real closed field R, mimicking the case R = R. We show that the typical ranks are the same if we take a larger real closed field and in particular that for every format (n1, . . . , ns) the typical ranks of tensors of format (n1, . . . , ns) are the same over R and over R. AMS Subject Classification: 14N05
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: Bollettino dell'Unione Matematica Italiana
سال: 2017
ISSN: 1972-6724,2198-2759
DOI: 10.1007/s40574-017-0134-0