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In mathematics, the distributive property of binary operations is a generalization of the distributive law, ... From the point of view of algebra, ...
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra. The term appears in William Betz's 1929 text Algebra for Today, where he states: [2]
A non-associative algebra [1] (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative.That is, an algebraic structure A is a non-associative algebra over a field K if it is a vector space over K and is equipped with a K-bilinear binary multiplication operation A × A → A which may or may not be associative.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, ... by the distributive property. [29] ...
2.1 Distributive properties. 2.2 First ... The generalization of the dot product formula to Riemannian manifolds is a defining property of a ... Vector algebra ...
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A T (among other notations). [1] The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. [2]
Elementary algebra, also known as high school algebra or college algebra, [1] ... Brackets can be "multiplied out", using the distributive property. For example, ...