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A homology class in a singular homology theory is represented by a finite linear combination of geometric subobjects with zero boundary. Such a linear combination is ...

Let a_1, a_2, ..., a_n be scalars not all equal to 0. Then the set S consisting of all vectors X=[x_1; x_2; |; x_n] in R^n such that a_1x_1+a_2x_2+...+a_nx_n=c for c a ...

Informally, a symplectic map is a map which preserves the sum of areas projected onto the set of (p_i,q_i) planes. It is the generalization of an area-preserving map. ...

The general orthogonal group GO_n(q,F) is the subgroup of all elements of the projective general linear group that fix the particular nonsingular quadratic form F. The ...

The conjecture that the Artin L-function of any n-dimensional complex representation of the Galois group of a finite extension of the rational numbers Q is an Artin ...

The word "normal form" is used in a variety of different ways in mathematics. In general, it refers to a way of representing objects so that, although each may have many ...

The so-called rule of three is an educational tool utilized historically to verbalize the process of solving basic linear equations with four terms where three of the terms ...

The Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly ...

A quadratic map is a quadratic recurrence equation of the form x_(n+1)=a_2x_n^2+a_1x_n+a_0. (1) While some quadratic maps are solvable in closed form (for example, the three ...

The word adjoint has a number of related meanings. In linear algebra, it refers to the conjugate transpose and is most commonly denoted A^(H). The analogous concept applied ...