Original sentence: The definition has been usefully extended to some non-numeric exponents, for instance as the matrix exponential or the exponential map.The exponential function has an analytic continuation which is an entire function, that is it has no singularity over the whole complex plane.The occurrence of the exponential function in Euler's formula gives it a central place when working with complex numbers
Edited sentence: Euler's formula relates its values at purely imaginary arguments to trigonometric functions.The exponential function also has analogues for which the argument is a matrix, or even an element of a Banach algebra or a Lie algebra.The exponential function extends to an entire function on the complex plane