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.

We say an Hermitian matrix $A$ is positive if $$ \bar{z}^tAz=\sum_{i,j=1}^na_{ij}\bar{z}_iz_j>0,\quad \forall z\neq 0.$$

But if we have $$z^tA\bar{z}=\sum_{i,j=1}^na_{ij}z_i\bar{z}_j>0,\quad \forall z\neq 0.$$ can we say that $A$ is positive? Prove or counterexample

Thanks!

share|improve this question
    
It is obviously true when $A$ is real. –  akkkk Apr 16 '12 at 14:05

1 Answer 1

up vote 3 down vote accepted

Replace $z$ in the second line by $w$ and then choose $w=\bar z$ to see that the two statements are equivalent.

share|improve this answer
    
Thanks! And I can't believe that I asked such a silly question! –  Y.Z Apr 16 '12 at 14:16

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.