Twoapplicationsofthetheoryofprimarymatrix functions Original Research Article

Among all the ways one might define f(A) for a square complex matrix A and a given function image , the notion of a primary matrix function is perhaps the most useful and natural. Using only basic conceptual properties of primary matrix functions, we consider whether f(A) can have rank one, and whether, for a given B, there is a unique A such that f(A)=B.