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Although the multiplication of one vector by another is not uniquely defined (cf. scalar multiplication, which is multiplication of a vector by a scalar), several types of ...

A convex polyhedron is defined as the set of solutions to a system of linear inequalities mx<=b (i.e., a matrix inequality), where m is a real s×d matrix and b is a real ...

A W^*-algebra is a C-*-algebra A for which there is a Banach space A_* such that its dual is A. Then the space A_* is uniquely defined and is called the pre-dual of A. Every ...

The matrix product of a square set of data d and a matrix of basis vectors consisting of Walsh functions. By taking advantage of the nested structure of the natural ordering ...

A curve named after James Watt (1736-1819), the Scottish engineer who developed the steam engine (MacTutor Archive). The curve is produced by a linkage of rods connecting two ...

A weak pseudo-Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is symmetric and for which, at each m in M, g_m(v_m,w_m)=0 for all w_m in T_mM implies ...

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

The version of set theory obtained if Axiom 6 of Zermelo-Fraenkel set theory is replaced by 6'. Selection axiom (or "axiom of subsets"): for any set-theoretic formula A(u), ...

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

Given two additive groups (or rings, or modules, or vector spaces) A and B, the map f:A-->B such that f(a)=0 for all a in A is called the zero map. It is a homomorphism in ...