Concept

Invariant factor

The invariant factors of a module over a principal ideal domain (PID) occur in one form of the structure theorem for finitely generated modules over a principal ideal domain. If is a PID and a finitely generated -module, then for some integer and a (possibly empty) list of nonzero elements for which . The nonnegative integer is called the free rank or Betti number of the module , while are the invariant factors of and are unique up to associatedness. The invariant factors of a matrix over a PID occur in the Smith normal form and provide a means of computing the structure of a module from a set of generators and relations.

Official source

https://en.wikipedia.org/wiki/Invariant_factor

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Related publications (1)

Conformational mobility and preferences of allyl-type organometallic intermediates. Dodec-2-enylpotassium

Manfred Schlosser

Alk-2-enylpotassium compds. having endo conformation are synthetically very valuable precursors of (Z)-olefinic derivs. substituted at the outward allylic position. They may be generated by "stereoconservative" metalation of the readily available (Z)-alk-2-enes by using the superbasic mixt. of BuLi and potassium tert-butoxide or by metalation under similar conditions of stereorandom mixts. of alk-2-enes or alk-1-enes followed by torsional isomerization of the concomitantly formed exo conformers to the the

1997

Related concepts (2)

Structure theorem for finitely generated modules over a principal ideal domain

In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules over a principal ideal domain (PID) can be uniquely decomposed in much the same way that integers have a prime factorization. The result provides a simple framework to understand various canonical form results for square matrices over fields.

Frobenius normal form

In linear algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices obtained by conjugation by invertible matrices over F. The form reflects a minimal decomposition of the vector space into subspaces that are cyclic for A (i.e., spanned by some vector and its repeated images under A). Since only one normal form can be reached from a given matrix (whence the "canonical"), a matrix B is similar to A if and only if it has the same rational canonical form as A.

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