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For any ideal I in a Dedekind ring, there is an ideal I_i such that II_i=z, (1) where z is a principal ideal, (i.e., an ideal of rank 1). Moreover, for a Dedekind ring with a ...

The subdiagonal of a square matrix is the set of elements directly under the elements comprising the diagonal. For example, in the following matrix, the diagonal elements are ...

A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor). To examine the transformation properties of a contravariant tensor, ...

The gonality (also called divisorial gonality) gon(G) of a (finite) graph G is the minimum degree of a rank 1 divisor on that graph. It can be thought of as the minimum ...

One of the four divisions of observations which have been grouped into four equal-sized sets based on their statistical rank. The quartile including the top statistically ...

The set of fixed points which do not move as a knot is transformed into itself is not a knot. The conjecture was proved in 1978 (Morgan and Bass 1984). According to Morgan ...

A technical mathematical object defined in terms of a polynomial ring of n variables over a field k. Syzygies occur in tensors at rank 5, 7, 8, and all higher ranks, and play ...

The term "similarity transformation" is used either to refer to a geometric similarity, or to a matrix transformation that results in a similarity. A similarity ...

A univariate distribution proportional to the F-distribution. If the vector d is Gaussian multivariate-distributed with zero mean and unit covariance matrix N_p(0,I) and M is ...

A generalized eigenvector for an n×n matrix A is a vector v for which (A-lambdaI)^kv=0 for some positive integer k in Z^+. Here, I denotes the n×n identity matrix. The ...