Exponential family
What is important to note, and what characterizes all exponential family variants, is that the parameter(s) and the observation variable(s) must factorize (can be separated into products each of which involves only one type of variable), either directly or within either part (the base or exponent) of an exponentiation operation. Generally, this means that all of the factors constituting the density or mass function must be of one of the following forms:
Exponentiation
Apart from matrices, more general linear operators can also be exponentiated. An example is the derivative operator of calculus, formula_142, which is a linear operator acting on functions formula_25 to give a new function formula_144. The "n"-th power of the differentiation operator is the "n"-th derivative: