title: Note: An explicit solution of the optimal superposition and Eckart frame problems.
abstract: Attention is called to an explicit solution of both the optimal superposition and Eckart frame problems that requires neither matrix diagonalization nor quaternion algebra. A simple change in one variable that enters the expression for the solution matrix T allows for selection of T representing either a proper rotation or a more general orthogonal transformation. The issues concerning the use of these alternative selections and the equivalence of the two problems are addressed.
authors.affiliation: Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland and Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany.
authors.forename: Jerzy
authors.initials: J
authors.lastname: Cioslowski