1
$\begingroup$

I have a matrix $A$ which is strictly lower triangular. Now, I am trying to find some general statements/relationships of following matrices $U,D,V,K$ defined as:

$AA^T=VKV^H$,

$[(I-A)(I-A)^T]^{-1}=UD^{-1}U^H$

Is it possible to put $D$ and $K$ into some relations and also $U$ and $V$? From simple examples it is possible to see much structure between $AA^T$ and $[(I-A)(I-A)^T)]^{-1}$, however, in "Matrix Analysis" by Horn & Johnson I was not able to find something useful for this case. Maybe someone has some great idea!

Many thanks in advance!

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ Since $A$ is strictly lower triangular, $A^n=0$, so $(I-A)^T=I+A+A^2+\dots+A^{n-1}$. This might be a good starting point. $\endgroup$
    – Wojowu
    Commented Jun 22, 2017 at 17:23

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .