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invariant set

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  • Positive invariant set — A positive invariant set is a set with the following properties:Given a system dot{x}=f(x) and trajectory x(t,x 0) , where x 0 , is the initial point. Let mathcal{O} riangleq left lbrace x in mathbb{R}^n| phi (x) = 0 ight brace where phi is a… …   Wikipedia

  • Invariant (mathematics) — In mathematics, an invariant is a property of a class of mathematical objects that remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually… …   Wikipedia

  • Set theory of the real line — is an area of mathematics concerned with the application of set theory to aspects of the real numbers. For example, one knows that all countable sets of reals are null, i.e. have Lebesgue measure 0; one might therefore ask the least possible size …   Wikipedia

  • Invariant estimator — In statistics, the concept of being an invariant estimator is a criterion that can be used to compare the properties of different estimators for the same quantity. It is a way of formalising the idea that an estimator should have certain… …   Wikipedia

  • Invariant subspace — In mathematics, an invariant subspace of a linear mapping : T : V rarr; V from some vector space V to itself is a subspace W of V such that T ( W ) is contained in W . An invariant subspace of T is also said to be T invariant.If W is T invariant …   Wikipedia

  • Set theory — This article is about the branch of mathematics. For musical set theory, see Set theory (music). A Venn diagram illustrating the intersection of two sets. Set theory is the branch of mathematics that studies sets, which are collections of objects …   Wikipedia

  • Invariant measure — In mathematics, an invariant measure is a measure that is preserved by some function. Invariant measures are of great interest in the study of dynamical systems. The Krylov Bogolyubov theorem proves the existence of invariant measures under… …   Wikipedia

  • Invariant subspace problem — In the field of mathematics known as functional analysis, one of the most prominent open problems is the invariant subspace problem, sometimes optimistically known as the invariant subspace conjecture. It is the question whether the following… …   Wikipedia

  • Invariant factor — The invariant factors of a module over a principal ideal domain occur in one form of the structure theorem for finitely generated modules over a principal ideal domain.If R is a PID and M a finitely generated R module, then:Mcong R^roplus R/(a… …   Wikipedia

  • Set theory (music) — Example of Z relation on two pitch sets analyzable as or derivable from Z17 (Schuijer 2008, p.99), with intervals between pitch classes labeled for ease of comparison between the two sets and their common interval vector, 212320. Musical set… …   Wikipedia

  • Scale-invariant feature transform — Feature detection Output of a typical corner detection algorithm …   Wikipedia

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