On Maximum, Typical, and Generic Ranks
نویسندگان
چکیده
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.
منابع مشابه
Capturing Outlines of Planar Generic Images by Simultaneous Curve Fitting and Sub-division
In this paper, a new technique has been designed to capture the outline of 2D shapes using cubic B´ezier curves. The proposed technique avoids the traditional method of optimizing the global squared fitting error and emphasizes the local control of data points. A maximum error has been determined to preserve the absolute fitting error less than a criterion and it administers the process of curv...
متن کاملA genre Analysis of the Scholarly Electronic Mail: Implications for Pedagogy
Scholarly mails apparently display stable conventional principles as an emerging genre. Thus, contributors should structure their electronic mails appropriately when writing for purposes of discussing professional topics. However, this requirement plunges many a scholar in dilemma as to how to go about this vital undertaking without written structural norms in electronic mail communication. Thi...
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 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 کاملOn the generic rank of 3-tensors
We study the generic rank of 3-tensors using results from matrices and algebraic geometry. We state a conjecture about the exact values of the generic rank of 3-tensors over the complex numbers. We also discuss generic ranks over the real numbers. 2000 Mathematics Subject Classification. 14A25, 14P10, 15A69.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1402.2371 شماره
صفحات -
تاریخ انتشار 2014