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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.

Classification

Nouns denoting groupings of people or objects.

Examples

  • The direct sum of two vector spaces V and W is a new vector space formed by taking the Cartesian product of V and W, and defining addition and scalar multiplication component-wise.
  • The direct sum of two groups G and H is an abelian group when both G and H are abelian.
  • In algebra, the tensor product and the direct sum are used to combine two algebraic structures.
  • Finite direct sums are used to define Hilbert spaces in functional analysis.
  • The direct sum is particularly useful for categorizing the finite simple groups in group theory.

Hypernyms

  • Join
  • Sum
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