Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Consider a Toeplitz matrix T which has both positive and negative eigenvalues. Can we prove that there exist two Toeplitz matrix T1 and T2 such that T1+T2=T and T1 has only one positive Eigenvalues and T2 has only negative Eigenvalues? Any reply would be appreciated. Regards

share|improve this question
    
Are you assuming your Toeplitz matrix is self-adjoint? –  Yemon Choi Aug 30 '12 at 23:33
    
The Toeplitz matrix considered is Hermitian matrix. Thank you for looking at my question. –  Rantu Aug 30 '12 at 23:41
1  
I think you need further conditions to make this interesting. You can take $T1 = T + \gamma I$, $T2 = - \gamma I$, where $\gamma$ is a large constant. This way, $T1$ will have only positive eigenvalues, and $T2$ will have negative ones (since you're shifting them by $\gamma$). –  coma Aug 30 '12 at 23:59
    
True. Thank you for your comment. I assumed constant norm or unchanged diagonal condition need to be apply. Thanks a lot. –  Rantu Aug 31 '12 at 0:07

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.