direct sum
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English
Noun
direct sum (plural direct sums)
- (mathematics) coproduct in some categories, like abelian groups, topological spaces or modules
- (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.
- (linear algebra) A block diagonal matrix interpreted as having its non-zero blocks (which are square matrices) as summands.[1][2][3]
Translations
coproduct in some categories
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References
- ^ 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
- ^ 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
- ^ 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
- (linear algebra):
Direct sum of modules on Wikipedia.Wikipedia
