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Let A be a normed (Banach) algebra. An algebraic left A-module X is said to be a normed (Banach) left A-module if X is a normed (Banach) space and the outer multiplication is ...

The set of octonions, also sometimes called Cayley numbers and denoted O, consists of the elements in a Cayley algebra. A typical octonion is of the form ...

The maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of ...

Qubic is a generalization of tic-tac-toe in which players alternately place pieces to get four in a row (rows, columns, pillars, face diagonals, or space diagonals) on a ...

The quotient space K^__1A=K_1A/{0,[-1]} of the Whitehead group K_1A is known as the reduced Whitehead group. Here, the element [-1] in K_1A denotes the order-2 element ...

A function f in C^infty(R^n) is called a Schwartz function if it goes to zero as |x|->infty faster than any inverse power of x, as do all its derivatives. That is, a function ...

Given a Hilbert space H, the sigma-strong operator topology is the topology on the algebra L(H) of bounded operators from H to itself defined as follows: A sequence S_i of ...

A Lie algebra g is solvable when its Lie algebra commutator series, or derived series, g^k vanishes for some k. Any nilpotent Lie algebra is solvable. The basic example is ...

In the above figure, the identical squares A, B, C appear different in width and height, because subdividing a space makes it appear larger. A different orientation can also ...

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y, (2) where x·y is vector multiplication which is assumed to be bilinear. Now define ...