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Let B, A, and e be square matrices with e small, and define B=A(I+e), (1) where I is the identity matrix. Then the inverse of B is approximately B^(-1)=(I-e)A^(-1). (2) This ...

A polynomial that represents integers for all integer values of the variables. An integer polynomial is a special case of such a polynomial. In general, every integer ...

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...

A linear transformation of period two. Since a linear transformation has the form, lambda^'=(alphalambda+beta)/(gammalambda+delta), (1) applying the transformation a second ...

An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an ...

Given a general second tensor rank tensor A_(ij) and a metric g_(ij), define theta = A_(ij)g^(ij)=A_i^i (1) omega^i = epsilon^(ijk)A_(jk) (2) sigma_(ij) = ...

Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or ...

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 ...

A quantity involving primitive cube roots of unity which can be used to solve the cubic equation.

The conjecture that the Artin L-function of any n-dimensional complex representation of the Galois group of a finite extension of the rational numbers Q is an Artin ...