Linearly dependent vectorial decomposition of clutters
نویسندگان
چکیده
منابع مشابه
Linearly dependent vectorial decomposition of clutters
This paper deals with the question of completing a monotone increasing family of subsets Γ of a finite set Ω to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we demonstrate that such vectorial completions of the family of subsets Γ exist and, in addition, we show that the minimal vectorial completions of the family Γ provide a decomposition of the...
متن کاملCompletion and Decomposition of a Clutter into Representable Matroids
This paper deals with the question of completing a monotone increasing family of subsets Γ of a finite set Ω to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove that such vectorial completions of the family of subsets Γ exist and, in addition, we show that the minimal vectorial completions of the family Γ provide a decomposition of the clutt...
متن کاملOn generic frequency decomposition. Part 1: Vectorial decomposition
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From this theory an entire branch of research has flourished: from the Short-Time or Windowed Fourier Transform to the Wavelets, the Frames, and lately the Gener...
متن کاملGraphical representations of clutters
We discuss the use of K-terminal networks to represent arbitrary clutters. A given clutter has many di¤erent representations, and there does not seem to be any set of simple transformations that can be used to transform one representation of a clutter into any other. We observe that for t 2 the class of clutters that can be represented using no more than t terminals is closed under minors, and ...
متن کاملLocally Linearly Dependent Operators
Let T be a linear operator defined on a complex vector space X and let n be a positive integer. Kaplansky [4] proved that T is algebraic of degree at most n if and only if for every x ∈ X the vectors x, Tx, . . . , Tnx are linearly dependent. One consequence of Kaplansky’s result is that if X is a Banach space and T : X → X a bounded linear operator, then T is algebraic if and only if for every...
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: Electronic Notes in Discrete Mathematics
سال: 2014
ISSN: 1571-0653
DOI: 10.1016/j.endm.2014.08.028