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The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...

The volume of a solid body is the amount of "space" it occupies. Volume has units of length cubed (i.e., cm^3, m^3, in^3, etc.) For example, the volume of a box (cuboid) of ...

The wedge product is the product in an exterior algebra. If alpha and beta are differential k-forms of degrees p and q, respectively, then alpha ^ beta=(-1)^(pq)beta ^ alpha. ...

Let (K,L) be a pair consisting of finite, connected CW-complexes where L is a subcomplex of K. Define the associated chain complex C(K,L) group-wise for each p by setting ...

The Wythoff array is an interspersion array that can be constructed by beginning with the Fibonacci numbers {F_2,F_3,F_4,F_5,...} in the first row and then building up ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements. Antichains are also called Sperner systems in older literature ...

The terms of equational logic are built up from variables and constants using function symbols (or operations). Identities (equalities) of the form s=t, (1) where s and t are ...

There are a number of mathematical curves that produced heart shapes, some of which are illustrated above. A "zeroth" curve is a rotated cardioid (whose name means ...

An irreducible representation of a group is a group representation that has no nontrivial invariant subspaces. For example, the orthogonal group O(n) has an irreducible ...