The matrizant and Saxon - Hutner theorem

Vector Parameters in Classical Hyperbolic Geometry

“…The first one, explicitly relying on Rodrigues' formula, was proposed by Davenport [9] and recently exploited by Piovan and Bullo [27] in a more consistent framework. The second one is based on the vector parameter construction, proposed by Rodrigues [29] and developed in the works of Gibbs [11], who used to call it "vector semitangent of version" (now it is commonly known as Gibbs' or Rodrigues' vector) and Fedorov [10], while two of the present authors are among the first to utilize it in classical mechanics [23,24] and certain quantum mechanical problems [19,20,22]. To our knowledge it was first exploited in the context of Euler decomposition by Wohlhart [34], but the idea was fully developed only recently in [5,21], where analytic solutions based on this construction are presented.…”

• An Algebraic Approach to Saxon-Hutner Theorem

“…Various conditions for the validity of the above statement are discussed in [4][5][6] and [9] in the context of one-dimensional quantum mechanics which will have in mind in this paper as well. For convenience from now on we denote the transfer matrices by A, B.…”