Abstract
A general formalism is given to construct a transformation matrix TAB which connects two matrices A and B of order n × n satisfying any given polynomial equations of degree r(≤n). The matrix TAB is given explicitly by a polynomial of degree (r − 1) in A and B. A special case where B is a diagonal matrix equivalent to A leads to a general theory of matrix diagonalization. The formalism contains the projection operator method as a special case. Illustrative examples are given on the Dirac theory of the electron and the basic 2 × 2 spinor representation of the proper orthochronous Lorentz group; the latter is completely prameterized by the spatial rotation and the velocity of the parallel translation.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
