How to Calculate the Exponential of Matrices
  How to calculate the exponential of matrices in an explicit manner is one of fundamental problems in almost all subjects in Science.   Especially in Mathematical Physics or Quantum Optics many problems are reduced to this calculation by making use of some approximations whether they are appropriate or not. However, it is in general not easy.   In this paper we give a very useful formula which is both elementary and getting on with computer. 
Kazuyuki Fujii and Hiroshi Oike