direct sum


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direct sum

[də¦rekt ′səm]
(mathematics)
If each of the sets in a finite direct product of sets has a group structure, this structure may be imposed on the direct product by defining the composition “componentwise”; the resulting group is called the direct sum.
References in periodicals archive ?
where the sum is over all direct sums [sigma] = [[?
explores advanced topics in direct sum decompositions of abelian groups and their consequences.
Equations (21) and (35) are expressions associated with the orthogonal direct sum decomposition [[?
The tangent space has the direct sum decomposition into subbundles:
q]-connection on a left U-module E, [pi] is the projection on the first summand in the direct sum M [direct sum] N, and [pi]([omega] [[cross product].
m,n] are injective and associative (in the sense that the external multiplication morphism they implement on the direct sum [[direct sum].
Let X, Y [subset] V be two subspaces of a vector space V such that X [intersection] Y = {0}, then their direct sum is denoted by X [direct sum] Y.
The analogy between the Hermitian direct sum operation and the honeycomb overlay operation is even tighter than this: at the critical values of "take eigenvalues" that are not at extrema, one also finds transverse overlays, and the index of the Hessian can be computed from the number of intersections that are clockwise.
By Haag, Lopuszanski, and Sohnius extension of Coleman-Mandula theorem [10] this representation is equivalent to the direct sum of N copies of the 4-dimensional spinor representation (Majorana spinor) [Q.
We can prove that the Drazin spectrum satisfies the spectral mapping theorem, and the Drazin spectrum of a direct sum is the union of the Drazin spectrum of the components.
It is not true that the direct sum of two Schubert varieties is an interval positroid variety.
By a crossed system we mean a quadruple {A, G, [sigma], [alpha]} where A is the direct sum of rings [A.

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