We present some insights on the relative error matrix between the process transfer function matrix and its diagonal matrix, which has been used in analyzing dynamic interactions by several authors. Proposed interaction measures can be interpreted in terms of differences of the complementary sensitivity function matrices when loops are closed, extending the concept of gain changes in the relative gain array. To employ the interaction measures, control systems are designed in advance using internal model control. With changes in the closed-loop time constant, proper pairings based on closed-loop response speeds can be obtained.