Batoric
Batoric is a term used in speculative mathematics and related fiction to describe a framework for studying symmetries that preserve a generalized energy form. In this usage, a batoric structure consists of a set X equipped with a symmetric bilinear form B: X × X → R, called the batoric form, and a collection of transformations f: X → X that satisfy B(f(u), f(v)) = B(u, v) for all u, v in X. Elements of this collection form a group under composition, often referred to as the Batoric group.
In finite-dimensional real vector spaces with B defined by a matrix M, the batoric group coincides with
Applications of the idea are primarily conceptual and educational. Batoric frameworks are used to illustrate invariants,
Origins of the term are informal and vary by author; batoric ideas have circulated in speculative literature
See also: Orthogonal group, Invariant theory, Bilinear form, Metric geometry.