Tricks of the Trade

Here is a simple trick for computing the complex conjugate of complex expressions involving real variables using a replacement rule.

A few special superscripts are not interpreted as powers (see sections 2.8.15 and 3.10.2 of The Mathematica Book), such as

We can program SuperStar to compute the conjugate.

Now conjugates can be computed using standard notation, as follows.

Since we can quickly and efficiently compute the absolute value of complex expressions involving real parameters.

Similarly, here is a rule for computing the Hermitian (matrix) adjoint using SuperDagger.

After introducing

it is easy to show that the following general matrix,

is Hermitian.

We conclude by clearing the definitions associated with SuperDagger, SuperStar, , , and Subscript.

Converted by Mathematica September 30, 1999