When studying complex numbers/vectors/functions and so forth you constantly encounter the idea of an inner product of two quantities (numbers/vectors/functions). It's represented as A*B is the inner product of two of these, but I've never been convinced why it couldn't also be AB*, as this is some cases yields a different answer. It seems arbitrary to me that it is defined in either way. Can someone explain to me the correct definition and also why it is correct? Any help would be much appreciated.