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Gives a matrix representation b_i of a braid group in terms of (n-1)×(n-1) matrices. A -t always appears in the (i,i) position. b_1 = [-t 0 0 ... 0; -1 1 0 ... 0; 0 0 1 ... ...

The product of a family {X_i}_(i in I) of objects of a category is an object P=product_(i in I)X_i, together with a family of morphisms {p_i:P->X_i}_(i in I) such that for ...

If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f degreesg is differentiable at x. Furthermore, let y=f(g(x)) and u=g(x), then ...

The term "closure" has various meanings in mathematics. The topological closure of a subset A of a topological space X is the smallest closed subset of X containing A. If R ...

Given a complex Hilbert space H with associated space L(H) of continuous linear operators from H to itself, the commutant M^' of an arbitrary subset M subset= L(H) is the ...

Let X and Y be sets, and let R subset= X×Y be a relation on X×Y. Then R is a concurrent relation if and only if for any finite subset F of X, there exists a single element p ...

A concise notation based on the concept of the tangle used by Conway (1967) to enumerate prime knots up to 11 crossings. An algebraic knot containing no negative signs in its ...

The categorical notion which is dual to product. The coproduct of a family {X_i}_(i in I) of objects of a category is an object C=coproduct_(i in I)X_i, together with a ...

The Doro graph is a distance-transitive and Distance-Regular Graph on 68 vertices and with valency 12. It is the unique automorphic graph having intersection array ...

The dual vector space to a real vector space V is the vector space of linear functions f:V->R, denoted V^*. In the dual of a complex vector space, the linear functions take ...