direct sum

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  • noun

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a union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets

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Using the Riesz idempotent E[lambda] with respect to [lambda], we can represent T as the direct sum [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
perpendicular to]]) is a direct sum, but in general not an orthogonal one.
E) of the covector fields on E decomposes in the direct sum
1 and 2] give recurrences that reduce the computation of the Mobius function [mu]([sigma], [tau]) to Mobius function calculations of the form [mu]([sigma]', [tau]') where [tau]' is a single component of [tau] and [sigma]' is a direct sum of consecutive components of [sigma].
As a result of this evaluation the national and regional totals will now be produced as a direct sum of the individual State totals (including the District of Columbia).
Direct sum decompositions of torsion-free finite rank groups.
Equation (27) is a (generally non-orthogonal) direct sum decomposition of [?
In [10], Uchiyama gives a matrix representation for a paranormal operator with respect to the direct sum of an eigenspace and its orthogonal complement.
It is actually a direct sum of two type A electrical Lie algebras.
Hereditary Noetherian prime rings may be the only non-commutative Noetherian rings whose projective modules, both finitely and infinitely generated, have nontrivial direct sum behavior and a structure theorem describing that behavior, say mathematicians Levy (U.
This, in turn, shall lead to a decomposition of the tangent space of the manifold into a direct sum of orthogonal subbundles.
They achieve positive results by placing restrictive hypotheses on only a small subset of the complement submodules and explain why direct sum decomposition of various kinds occurs.
n] can be written as the direct sum of some irreducible representations [S.
presents an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization.
The operation [direct sum]: the direct sum of functions in the algebra of functions is similar to logic multiplication of the corresponding binary vectors components (operation AND) in the structural approach, i.
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