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Exponential Of A Matrix
 Syntax `expmat(`A`, `tol`, `mstep`)` See Also exp , odepade

Description
Returns the matrix exponential of A, where A is a real, double-precision, or complex matrix square matrix , tol is a real or double-precision scalar specifying the desired absolute accuracy in each element, mstep is an integer greater than 1 that specifies the base 2 logarithm of the maximum number of steps to use before giving up on the desired accuracy. The return value has the same type and dimension as A. ``` ```The matrix exponential of `A` is defined by ```               2        3      I + A + A / 2! + A / 3! + ... ```where the powers represent matrix multiplication.

Example ```      x = {[1., 0.], [0., 2.]}      tol = 1e-4      mstep = 6      expmat(x, tol, mstep) ``` returns ```      {      [ 2.71828 , 0 ]      [ 0 , 7.38906 ]      } ``` Note that for diagonal matrices the matrix exponential is the scalar exponential of the diagonal elements and the scalar exponential of 1 and 2 are 2.71828 and 7.38906, respectively.