Are you able to solve this Simple Matrix Challenge?

[blurking132]

I am working with 2 by 2 matrices, L, X, P and T.

L = PTP -------Eqn 1
X = PTTTTTTP ----------Eqn 2

where L and X are known matrices. P and T matrix are unknown and are to be solved.

The above problem looks simple but are you able to solve it?

 

[g_edgar]

Can you do a simple special case? for example

$$L = \left[1, 0; 0, 1\right], X = \left[0, 1; 0, 0\right]$$

 

[blurking132]

Let's use some numbers as an illustration.
For example,
P = [1 1;1 1]; T = [ 1 2;3 4 ];
L = P*T*P = [10 10;10 10];
X = P*T*T*T*T*T*T*P = [44966 44966;44966 44966];

We only have L and X. The problem is how to get back P and T.

 

[danong]

it seems to be solving some linearlity problem,
however this question can lead to ambiguos solutions,
i assume your question is bound to only by setting the P to be [1,1;1,1],
otherwise this question is meaningless.

i don't know, perhaps I'm wrong? why don't you propose your solution since you're confident and done some research?

 

[HallsofIvy]

If it were L= PTP^-1, the problem would be simple. But with L= PTP, ...

 

[danong]

and i doubted that if the elements within changed,
would it still be "simple" ?

for e.g, complex element, exponential, differential variable?


And it definitely not 'simple' as it looks,
from the first view it is already harzardous.

 

[0xDEADBEEF]

I am sorry to tell you that your problem is under defined. Even if we assume all matrices to be invertible you will get the same equations if you substitute P for -P.