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The term "transition matrix" is used in a number of different contexts in mathematics. In linear algebra, it is sometimes used to mean a change of coordinates matrix. In the ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Over a region D in the plane with boundary partialD, Green's theorem states ...

Any real function u(x,y) with continuous second partial derivatives which satisfies Laplace's equation, del ^2u(x,y)=0, (1) is called a harmonic function. Harmonic functions ...

"Escher's solid" is the solid illustrated on the right pedestal in M. C. Escher's Waterfall woodcut (Bool et al. 1982, p. 323). It is obtained by augmenting a rhombic ...

The notion of a Hilbert C^*-module is a generalization of the notion of a Hilbert space. The first use of such objects was made by Kaplansky (1953). The research on Hilbert ...

A simplex, sometimes called a hypertetrahedron (Buekenhout and Parker 1998), is the generalization of a tetrahedral region of space to n dimensions. The boundary of a ...

The base manifold in a bundle is analogous to the domain for a set of functions. In fact, a bundle, by definition, comes with a map to the base manifold, often called pi or ...

The Frobenius norm, sometimes also called the Euclidean norm (a term unfortunately also used for the vector L^2-norm), is matrix norm of an m×n matrix A defined as the square ...

Doob (1996) defines a stochastic process as a family of random variables {x(t,-),t in J} from some probability space (S,S,P) into a state space (S^',S^'). Here, J is the ...