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A rewriting of a given quantity (e.g., a matrix) in terms of a combination of "simpler" quantities.

The study of definable sets and functions in polish spaces.

For {M_i}_(i in I) a family of R-modules indexed by a directed set I, let sigma_(ij):M_i->M_j i<=j be an R-module homomorphism. Call (M_i,sigma_(ij)) a direct system over I ...

A number of attractive 7-compounds of the regular dodecahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

The double bar symbol | is used to denote certain kinds of norms in mathematics (e.g., ||x|| or ||x||_2). It is also used to denote parallel lines, as in A∥B, and in an older ...

Let A, B, and C be three polar vectors, and define V_(ijk) = |A_i B_i C_i; A_j B_j C_j; A_k B_k C_k| (1) = det[A B C], (2) where det is the determinant. The V_(ijk) is a ...

If x is a member of a set A, then x is said to be an element of A, written x in A. If x is not an element of A, this is written x not in A. The term element also refers to a ...

A singular point a for which f(z)(z-a)^n is not differentiable for any integer n>0.

A three-dimensional shadow of a four-dimensional Klein bottle.

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...