Hi, 1. The problem statement, all variables and given/known data I recently started delving into tensor calculus and am quite the stuck with the following: Given the tensor Ai = (x+y, y-x, z)i in cartesian coordinates, what would be the second covariant coordinate in cylindrical coordinates? AND Given the tensor Aij = (-1 0, -1 1)ij and the metric gij = (2 3, 3 4)ij, what would be A21? 2. Relevant equations 3. The attempt at a solution First, aren't I actually expected to find y-x in cylindrical coordinates, which is rsinθ - rcosθ? I have found the metric to be (1 0 0, 0 r2 0, 0 0 1), but I am really not sure how to put all the pieces together and how to proceed. Next, for finding A21 won't I actually need to multiply the given matrix by the metric and its inverse, thus yielding a similar matrix as the original? I could use some guidance, please.