direct sum

English

Noun

direct sum (plural direct sums)

  1. (mathematics) coproduct in some categories, like abelian groups, topological spaces or modules
  2. (linear algebra) A linear sum in which the intersection of the summands has dimension zero. Equivalently, a linear sum of two subspaces, any vector of which can be expressed uniquely as a sum of two vectors: one vector belonging to the first subspace, and the other vector belonging to the second subspace.
  3. (linear algebra) A block diagonal matrix interpreted as having its non-zero blocks (which are square matrices) as summands.[1][2][3]

Translations

References
  1. Garrett Birkhoff with Saunders Mac Lane (©1953) A Survey Of Modern Algebra, Revised edition, U.S.A.: The Macmillan Company, published 1960 (9th printing), §X.8, page 326
  2. David Steven Dummit with Richard M. Foote (©2004) Abstract Algebra, third edition, U.S.A.: John Wiley & Sons, Inc., →ISBN, →OCLC, §12.2, page 475
  3. Kenneth Myron Hoffman with Ray Alden Kunze (©1971) Linear Algebra, second edition, Upper Saddle River, New Jersey: Prentice-Hall, Inc., →ISBN, →OCLC, §6.7, page 214

Further reading
This article is issued from Wiktionary. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.