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invariant form

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  • Invariant theory — is a branch of abstract algebra that studies actions of groups on algebraic varieties from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of polynomial functions that do not …   Wikipedia

  • Invariant differential operators — appear often in mathematics and theoretical physics. There is no universal definition for them and the meaning of invariance may depend on the context. Usually, an invariant differential operator D is a map from some mathematical objects… …   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

  • 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 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

  • Invariant basis number — In mathematics, the invariant basis number (IBN) property of a ring R is the property that all free modules over R are similarly well behaved as vector spaces, with respect to the uniqueness of their ranks. Definition A ring R has invariant basis …   Wikipedia

  • invariant noun — noun A noun in which number is not marked; that is, a noun which does not change form in the plural, such as, in English, and …   Wiktionary

  • Volume form — In mathematics, a volume form is a nowhere zero differential n form on an n manifold. Every volume form defines a measure on the manifold, and thus a means to calculate volumes in a generalized sense. A manifold has a volume form if and only if… …   Wikipedia

  • Killing form — In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and Lie algebras. In an example of Stigler s law of eponymy, the Killing form was actually invented… …   Wikipedia

  • Jordan normal form — In linear algebra, a Jordan normal form (often called Jordan canonical form)[1] of a linear operator on a finite dimensional vector space is an upper triangular matrix of a particular form called Jordan matrix, representing the operator on some… …   Wikipedia

  • Maurer–Cartan form — In mathematics, the Maurer–Cartan form for a Lie group G is a distinguished differential one form on G that carries the basic infinitesimal information about the structure of G. It was much used by Élie Cartan as a basic ingredient of his method… …   Wikipedia

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