MORE EXPLICIT FORMULAS FOR THE MATRIX EXPONENTIAL

The matrix exponential plays an important role in the study of dynamic al systems and linear systems. An elementary method is discussed for c omputing e(tA) for general A is an element of C-n X n. It is shown tha t this method can be applied to generate explicit formulas for e(tA) i n various forms. Using this method, some well-known formulas are reder ived, and some new formulas are also derived. As applications, explici t formulas for n = 3 or n = 4 are given. In each case, a characterizat ion of e(tA) is also made, based on the entries of A alone. (C) Elsevi er Science Inc., 1997.