Thread Subject:

eigenvectors

Hello,

I have 2 matrices, A1 and A2 which are both 5x5

A1 = P1*Z1 + Q1 and
A2 = P2*Z2 + Q2

where P1 (5x2), P2(5x1), Q1 (5x5), and Q2 (5x5) are known matrices but Z1 (2x5) and Z2(1x5) are unknown matrices.

Are there any methods to choose suitable Z1 and Z2 so that A1 and A2 have the same eigenvectors?

Thanks a lot.

Frank

"Frank " <allinone_2003@yahoo.com.hk> wrote in message <ka1bes$dcs$1@newscl01ah.mathworks.com>...
> Hello,
>
> I have 2 matrices, A1 and A2 which are both 5x5
>
> A1 = P1*Z1 + Q1 and
> A2 = P2*Z2 + Q2
>
> where P1 (5x2), P2(5x1), Q1 (5x5), and Q2 (5x5) are known matrices but Z1 (2x5) and Z2(1x5) are unknown matrices.
>
> Are there any methods to choose suitable Z1 and Z2 so that A1 and A2 have the same eigenvectors?

Not possible in general.

Bruno