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An antisymmetric matrix, also known as a skew-symmetric or antimetric matrix, is a square matrix that satisfies the identity A=-A^(T) (1) where A^(T) is the matrix transpose. ...

If A is a normed algebra, a net {e_i} in A is called an approximate identity for A if sup_(i)|e_i|<infty and if for each a in A, e_ia->a and ae_i->a. Though this definition ...

Given a module M over a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the associated graded module of M with ...

Given a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the associated graded ring of R with respect to F is the ...

Polynomials b_n(x) which form a Sheffer sequence with g(t) = t/(e^t-1) (1) f(t) = e^t-1, (2) giving generating function sum_(k=0)^infty(b_k(x))/(k!)t^k=(t(t+1)^x)/(ln(1+t)). ...

Let A and B be two algebras over the same signature Sigma, with carriers A and B, respectively (cf. universal algebra). B is a subalgebra of A if B subset= A and every ...

Let s(x,y,z) and t(x,y,z) be differentiable scalar functions defined at all points on a surface S. In computer graphics, the functions s and t often represent texture ...

The qubit |psi>=a|0>+b|1> can be represented as a point (theta,phi) on a unit sphere called the Bloch sphere. Define the angles theta and phi by letting a=cos(theta/2) and ...

A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable ...

Letting Lk be the linking number of the two components of a ribbon, Tw be the twist, and Wr be the writhe, then Lk(K)=Tw(K)+Wr(K). (Adams 1994, p. 187).