Linear combination of vectors

May 29th, 2015
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Subspace: A subset W of a vector space V over a field F is called a subspace of V if W is a vector space over F with the operations of additions and scalar multiplication defined on V. Let V be a vector space and W a subset of V. Then W is a

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Boolean algebra (structure)From Wikipedia, the free encyclopediaJump to: navigation, searchFor an introduction to the subject, see Boolean algebra#Boolean algebras. For the elementary syntax and axiomatics of the subject, see Boolean algebra. For an alternative presentation, see Boolean algebras canonically defined.It has been suggested that two-element Boolean algebra be merged into this article or section. (Discuss) Proposed since April 2011. In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets. It is also a special case of De Morgan algebra and Kleene algebra.Boolean lattice of subsetsContents[hide] 1 History2 Definition3 Examples4 Homomorphisms and isomorphisms5 Boolean rings6 Ideals and filters7 Representations8 Axiomatics9 Generalizations10 See also11 Notes12 References13 External links[edit] HistoryThe term "Boolean algebra" honors George Boole (18151864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854. Boole's formula

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