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The dimension of a partially ordered set P=(X,<=) is the size of the smallest realizer of P. Equivalently, it is the smallest integer d such that P is isomorphic to a ...

The contravariant four-vector arising in special and general relativity, x^mu=[x^0; x^1; x^2; x^3]=[ct; x; y; z], (1) where c is the speed of light and t is time. ...

A quantity x>0, which may be written with an explicit plus sign for emphasis, +x.

A positive definite function f on a group G is a function for which the matrix {f(x_ix_j^(-1))} is always positive semidefinite Hermitian.

A sequence {mu_n}_(n=0)^infty is positive definite if the moment of every nonnegative polynomial which is not identically zero is greater than zero (Widder 1941, p. 132). ...

Let A be a C^*-algebra, then a linear functional f on A is said to be positive if it is a positive map, that is f(a)>=0 for all a in A_+. Every positive linear functional is ...

Let A and B be C^*-algebras, then a linear map phi:A->B is said to be positive if phi(A_+) subset= B_+. Here, A_+ is denoted the positive part of A. For example, every ...

A positive matrix is a real or integer matrix (a)_(ij) for which each matrix element is a positive number, i.e., a_(ij)>0 for all i, j. Positive matrices are therefore a ...

A positive measure is a measure which is a function from the measurable sets of a measure space to the nonnegative real numbers. Sometimes, this is what is meant by measure, ...

Let f:R->R, then the positive part of f is the function f^+:R->R defined by f^+(x)=max(f(x),0) The positive part satisfies the identity f=f^+-f^-, where f^- is the negative ...