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The cokernel of a group homomorphism f:A-->B of Abelian groups (modules, or abstract vector spaces) is the quotient group (quotient module or quotient space, respectively) ...

If A is an n×n square matrix and lambda is an eigenvalue of A, then the union of the zero vector 0 and the set of all eigenvectors corresponding to eigenvalues lambda is ...

The degree (or relative degree, or index) of an extension field K/F, denoted [K:F], is the dimension of K as a vector space over F, i.e., [K:F]=dim_FK. If [K:F] is finite, ...

f(I) is the collection of all real-valued continuous functions defined on some interval I. f^((n))(I) is the collection of all functions in f(I) with continuous nth ...

A polynomial factorization algorithm that proceeds by considering the vector of coefficients of a polynomial P, calculating b_i=P(i)/a_i, constructing the Lagrange ...

Let M subset R^3 be a regular surface and u_(p) a unit tangent vector to M, and let Pi(u_(p),N(p)) be the plane determined by u_(p) and the normal to the surface N(p). Then ...

A regular local ring is a local ring R with maximal ideal m so that m can be generated with exactly d elements where d is the Krull dimension of the ring R. Equivalently, R ...

If pi on V and pi^' on V^' are irreducible representations and E:V|->V^' is a linear map such that pi^'(g)E=Epi(g) for all g in and group G, then E=0 or E is invertible. ...

A subset A of a vector space V is said to be convex if lambdax+(1-lambda)y for all vectors x,y in A, and all scalars lambda in [0,1]. Via induction, this can be seen to be ...

A linear real-valued function omega^1 of vectors v such that omega^1(v)|->R. Vectors (i.e., contravariant vectors or "kets" |psi>) and one-forms (i.e., covariant vectors or ...