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.

I have a matrix equation that reads: $T^{-1} A ( T^{\mathrm{T}} )^{-1} =D$ where $D$ is a diagonal matrix.

Can I conclude that $T^{-1} = T^{\mathrm{T}}$ and that $T$ is the matrix of the eigenvectors of $A$?

Thanks!

share|improve this question
3  
"0% accept rate" in bold red should alert you that its not OK not to accept any answers –  Belgi Sep 10 '12 at 18:43
    
Why doesnt the LaTeX code show up? This is very irritating, and especially the code in this question is about impossible to read! –  kjetil b halvorsen Sep 10 '12 at 19:01
    
I tried a few simplifications to try to get it to go, but it doesn't seem to want to budge... For example, I tried \mathsf in a field elsewhere, and it didn't render, so that's gone. –  rschwieb Sep 10 '12 at 19:14
    
By "can I do <random thing>" I guess you are wishing that this would work. Perhaps the problem that led you up to this would be useful? Along with any work you've already done? –  rschwieb Sep 10 '12 at 19:17
    
I gather there are mathjax issues at the moment due to some godaddy problems... –  copper.hat Sep 10 '12 at 19:22
show 1 more comment

1 Answer

up vote 3 down vote accepted

No.

Let $D$ be the identity matrix, $T=\begin{bmatrix}1&1\\0&1\end{bmatrix}$ and $A=\begin{bmatrix}2&1\\1&1\end{bmatrix}$.

Then you can compute that $TDT^T=A$, but $T^{-1}\neq T^T$.

share|improve this answer
add comment

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.