From a bit of Googling I found that the expm package has a matrix exponentiation function. With that in mind I think this does what you were asking for:

Let me know if I misunderstood. I'd be interested to know about the application you're using this for; when I was reading this I originally thought you meant something to generate Vandermonde matrices, but that's not what this is.

The thing is that im trying to find A , to find the matrix A that will give me the target matrix (that i already know). So the goal is to find A not the target matrix

OK so the inverse process to the code I gave before. Do you have an algorithm in mind that you need to get an implementation for in R, or are you looking for an algorithm to find A? If it's the latter then that's more of a maths question and so this probably isn't the best place. Cheers,