This paper is a survey of the literature on ways in which the concept of ordering can be extended to the setting of a division ring with involution and the main results for these extensions.

A general mathematical formulation of the n × n proper Orthogonal matrix, that corresponds to a rigid rotation in n-dimensional real Euclidean space, is given here. It is shown that a rigid rotation depends on an angle (principal angle) and on a set of (n−2) principal axes. The latter, however, can be more conveniently replaced by only 2 Orthogonal directions that identify the plane of rotation...

We prove that we can always construct strongly minimal linearizations of an arbitrary rational matrix from its Laurent expansion around the point at infinity, which happens to be case for polynomial matrices expressed in monomial basis. If has a particular self-conjugate structure, show how preserve it. The structures are considered Hermitian and skew-Hermitian with respect real line, para-Herm...