More explicit formulas for the matrix exponential

The matrix exponential plays an important role in the study of dynamical systems and linear systems. An elementary method is discussed for computing e(tA) for general A is an element of C-n X n. It is shown that this method can be applied to generate explicit formulas for e(tA) in various forms. Using this method, some well-known formulas are rederived, and some new formulas are also derived. As applications, explicit formulas for n = 3 or n = 4 are given. In each case, a characterization of e(tA) is also made, based on the entries of A alone. (C) Elsevier Science Inc., 1997.