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Given a matrix A, a Jordan basis satisfies Ab_(i,1)=lambda_ib_(i,1) and Ab_(i,j)=lambda_ib_(i,j)+b_(i,j-1), and provides the means by which any complex matrix A can be ...

The function Pi_(a,b)(x)=H(x-a)-H(x-b) which is equal to 1 for a<=x<=b and 0 otherwise. Here H(x) is the Heaviside step function. The special case Pi_(-1/2,1/2)(x) gives the ...

A database can be roughly defined as a structure consisting of 1. A collection of information (the data), 2. A collection of queries that can be submitted, and 3. A ...

Down arrow notation is an inverse of the Knuth up-arrow notation defined by evn = lnn (1) evvn = ln^*n (2) evvvn = ln^(**)n, (3) where ln^*n is the number of times the ...

A 1-factor of a graph G with n graph vertices is a set of n/2 separate graph edges which collectively contain all n of the graph vertices of G among their endpoints.

In a lattice, any two elements a and b have a least upper bound. This least upper bound is often called the join of a and b, and is denoted by a v b. One can also speak of ...

The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another equivalent description is that it is the intersection of the prime ...

The notation Q^_ denotes the algebraic closure of the rational numbers Q. This is equivalent to the set of algebraic numbers, sometimes denoted A.

If N is a submodule of the module M over the ring R, the quotient group M/N has a natural structure of R-module with the product defined by a(x+N)=ax+N for all a in R and all ...

A Greek cross rotated by 45 degrees, also called the crux decussata, illustrated schematically above in polyomino form. The multiplication sign × is based on Saint Andrew's ...