Let V be a finite dimensional complex inner product space with inner product < , >. Let U be unitary with respect to this inner product. If ( , ) is another inner product, is U also unitary with respect to ( , )?(adsbygoogle = window.adsbygoogle || []).push({});

The definition of unitary I'm working with is the one that says: U is unitary if <Uv, Uw> = <v w>, i.e. it preserves inner products.

Now it is easy to show that U is unitary with respect to < , > if and only if U'U = 1, where U' is the adjoint and 1 is the identity transformations. But by replacing < , > with ( , ), the prior statement says that U is also unitary with respect to ( , ).

Am I missing something?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Unitarity and Inner Products

**Physics Forums | Science Articles, Homework Help, Discussion**