direct sum

Noun

Meaning

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

Synonyms

Hypernyms

Examples

A "finite" direct product may also be viewed as a direct sum of ideals. Source: Internet

By the fundamental theorem of finitely generated abelian groups it is therefore a finite direct sum of copies of Z and finite cyclic groups. Source: Internet

Classification The fundamental theorem of finite abelian groups states that every finite abelian group G can be expressed as the direct sum of cyclic subgroups of prime -power order. Source: Internet

A variant of this construction is the direct sum (also called coproduct and denoted ), where only tuples with finitely many nonzero vectors are allowed. Source: Internet

But if there are only finitely many summands, then the Banach space direct sum is isomorphic to the Hilbert space direct sum, although the norm will be different. Source: Internet

Direct product and direct sum main The direct product of vector spaces and the direct sum of vector spaces are two ways of combining an indexed family of vector spaces into a new vector space. Source: Internet

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