In this talk we introduce two transformations of an arbitrary square matrix M into two new matrices, its power-dual pd(M) and its exponential-dual ed(M). Their interest is that the powers of M (resp. the exponential exp(M) -- or the function exp(Mt) with t scalar) can be obtained by evaluating the powers of its power-dual (resp. the exponential of its exponential-dual). The cost of finding, for instance, exp(M) in terms of exp(ed(M)), is low (linear). There are examples (for instance in Markov chain analysis) where these transformations can make the evaluation of powers or of exponentials easier than working with the original matrix. When M is the probability transition matrix -- p.t.m. (resp. the infinitesimal generator -- i.g.) of a Discrete (resp. of a Continuous) Time Markov Chain X, and if the Sigmund dual X^* of X exists, then the p.t.m. (resp. the i.g.) of X^* is the power-dual (resp. the exponential-dual) of M. So, they are generalizations of Sigmund duality to arbitrary matrices, showing that their properties are of algebraic nature. We describe the main properties of these transforms, and provide some examples of their applications.