Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How can it be shown that $UU^{*} = I$ where $U$ is a square matrix of an operator on a complex vector space implies that $\langle Ux, Uy\rangle = \langle x, y\rangle$?

share|improve this question

1 Answer 1

up vote 0 down vote accepted

Hint: For adjoint operators you have $$(Ax,y)=(x,A^{*}y)$$

share|improve this answer
    
You may try to expand the summation as $(UX,UY)=\sum_{i}(\sum_{j}u_{ij}x_{j}\overline{\sum_{j}u_{ij}y_{j}})$, etc. But this is usually quite messy. –  Kerry Oct 10 '11 at 17:06

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.