1. The problem statement, all variables and given/known data Y = AX = g(X) Where X,Y are elements of R^n and A is a nxn matrix. What is the Jacobian of this transformation, Jg(x)? 2. Relevant equations N.A. 3. The attempt at a solution Well, I know what to do in the non-matrix case. For example... U = g(x,y) V = h(x,y) The transformation can be seen as a vector valued function f(x,y) = (g(x,y),h(x,y)). So the jacobian of this transform, Jf(x,y) = the determinant of a matrix with row 1 = [dg/dx , dh/dx] and row 2 = [dg/dy, dh/dy]. So Jf(x,y) = (dg/dx)(dh/dy) - (dg/dy)(dh/dx). But what do I do in the matrix case? I know g(X) can be seen as a vector with functions as entries but does this help? Y = AX = g(X) = (g1(X),g2(X),...,gn(X)) Thanks!