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In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality. is always true in elementary algebra . For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition . This basic property of numbers is part of the ...
Dot product. In mathematics, the dot product or scalar product [note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors ), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or ...
e. In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain ), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An algebraic structure may be based on ...
A free ring satisfies the universal property: any function from the set X to a ring R factors through F so that F → R is the unique ring homomorphism. Just as in the group case, every ring can be represented as a quotient of a free ring. Now, we can impose relations among symbols in X by taking a quotient.
NAND logic. The NAND Boolean function has the property of functional completeness. This means that any Boolean expression can be re-expressed by an equivalent expression utilizing only NAND operations. For example, the function NOT (x) may be equivalently expressed as NAND (x,x). In the field of digital electronic circuits, this implies that it ...
Linear subspace. One-dimensional subspaces in the two-dimensional vector space over the finite field F5. The origin (0, 0), marked with green circles, belongs to any of six 1-subspaces, while each of 24 remaining points belongs to exactly one; a property which holds for 1-subspaces over any field and in all dimensions.
The continuous dual space of a topological vector space (TVS) X is denoted by X '. If X and Y are TVSs then a linear map u : X → Y is weakly continuous if and only if u#(Y ') ⊆ X ', in which case we let tu : Y ' → X ' denote the restriction of u# to Y '. The map tu is called the transpose [11] of u.
Distributive lattice. In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection.