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Given a real m×n matrix A, there are four associated vector subspaces which are known colloquially as its fundamental subspaces, namely the column spaces and the null spaces ...

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

Given a differential p-form q in the exterior algebra ^ ^pV^*, its envelope is the smallest subspace W such that q is in the subspace ^ ^pW^* subset ^ ^pV^*. Alternatively, W ...

Let A be a commutative ring and let C_r be an R-module for r=0,1,2,.... A chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0 is said to ...

There are two completely different definitions of Cayley numbers. The first and most commonly encountered type of Cayley number is the eight elements in a Cayley algebra, ...

The number of nonassociative n-products with k elements preceding the rightmost left parameter is F(n,k) = F(n-1,k)+F(n-1,k-1) (1) = (n+k-2; k)-(n+k-1; k-1), (2) where (n; k) ...

Let A be a finite-dimensional power-associative algebra, then A is the vector space direct sum A=A_(11)+A_(10)+A_(01)+A_(00), where A_(ij), with i,j=0,1 is the subspace of A ...

Noncommutative topology is a recent program having important and deep applications in several branches of mathematics and mathematical physics. Because every commutative ...

In general, a cross is a figure formed by two intersecting line segments. In linear algebra, a cross is defined as a set of n mutually perpendicular pairs of vectors of equal ...

A type of number involving the roots of unity which was developed by Kummer while trying to solve Fermat's last theorem. Although factorization over the integers is unique ...