# Are you able to solve this Simple Matrix Challenge?

1. Jun 28, 2009

### 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?

2. Jun 28, 2009

### g_edgar

Can you do a simple special case? for example

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

3. Jun 28, 2009

### 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.

4. Jun 29, 2009

### 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?

5. Jun 29, 2009

### HallsofIvy

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

6. Jun 29, 2009

### 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.

7. Jun 29, 2009

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.