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An extension of a group H by a group N is a group G with a normal subgroup M such that M=N and G/M=H. This information can be encoded into a short exact sequence of groups ...

Two planes that do not intersect are said to be parallel. Two planes specified in Hessian normal form are parallel iff |n_1^^·n_2^^|=1 or n_1^^xn_2^^=0 (Gellert et al. 1989, ...

Consider a formula in prenex normal form, Q_1x_1...Q_nx_nN. If Q_i is the existential quantifier (1<=i<=n) and x_k, ..., x_m are all the universal quantifier variables such ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method (MINRES) and ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method and symmetric LQ ...

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 ...