We consider first the analogue of the scalar, or dot product for . Recall first that if , then the conjugate of is the vector that results from applying complex conjugation degreewise Then the scalar product for is given by
[Note: The order in which the vectors are written here is the reverse of what it is in the real case. The reason is one of mathematical convention - for complex vectors (and matrices more generally) the analogue of the transpose is the conjugate-transpose. So these operations should be applied to the same vector (as in the expression appearing as the middle term) rather than separate vectors (as in the right-most term). Secondly, it is conventional to have the conjugation operator apply to the second vector rather than the first vector . However, this convention is not universal.]