Ads
related to: short exact sequence examples of linearstudy.com has been visited by 100K+ users in the past month
generationgenius.com has been visited by 10K+ users in the past month
Search results
Results From The WOW.Com Content Network
If we take a series of short exact sequences linked by chain complexes (that is, a short exact sequence of chain complexes, or from another point of view, a chain complex of short exact sequences), then we can derive from this a long exact sequence (that is, an exact sequence indexed by the natural numbers) on homology by application of the zig ...
If any of these statements holds, the sequence is called a split exact sequence, and the sequence is said to split. In the above short exact sequence, where the sequence splits, it allows one to refine the first isomorphism theorem, which states that: C ≅ B/ker r ≅ B/q(A) (i.e., C isomorphic to the coimage of r or cokernel of q) to:
An exact sequence (or exact complex) is a chain complex whose homology groups are all zero. This means all closed elements in the complex are exact. A short exact sequence is a bounded exact sequence in which only the groups A k, A k+1, A k+2 may be nonzero. For example, the following chain complex is a short exact sequence.
In mathematics, the Atiyah algebroid, or Atiyah sequence, of a principal -bundle over a manifold, where is a Lie group, is the Lie algebroid of the gauge groupoid of . Explicitly, it is given by the following short exact sequence of vector bundles over M {\displaystyle M} :
For the explicit examples, the relevant structures are supposedly in place. ... A short exact sequence is an exact sequence of length three, ... Let l be a linear map ...
The term split exact sequence is used in two different ways by different people. Some people mean a short exact sequence that right-splits (thus corresponding to a semidirect product) and some people mean a short exact sequence that left-splits (which implies it right-splits, and corresponds to a direct product). This article takes the latter ...
Relation between the projective special linear group PSL and the projective general linear group PGL; each row and column is a short exact sequence. The set (F *) n here is the set of nth powers of the multiplicative group of F.
Another example is the quotient of R n by the subspace spanned by the ... This relationship is neatly summarized by the short exact sequence ... Linear Algebra Done ...