Finding unknown matrix

• Dec 2nd 2012, 11:44 PM
skhan87
Finding unknown matrix
Hello guys,

I am having problem in finding an unknown matrix from matrix multiplication

Right now I am at this point

X . Y = Y . Z

Where X,Y and Z are 2x2 matrices. Among these X and Z are known and I have to compute Y.
I am trying to solve it by element by element multiplication, supposing Y = [y11 y12;y21 y22]

Can anyone tell me exact method or alternate equality of this relation what I mentioned above?

Thanks (Nod)
• Dec 3rd 2012, 05:45 PM
zhandele
Re: Finding unknown matrix
As I understand you, you don't know anything about the entries in X Y or Z? Are you given any further information?

If Y is invertible, then you can right-multiply each side by the inverse of Y and then X will be similar to Z.

One solution: if Y is the zero matrix, the equation will always be true. If X = Z, then Y is the identity matrix, or some other matrix with which X commutes. The most general rule I know of is that two matrices will commute iff they are both diagonalizable to the same basis. Some 2x2 matrices, of course, are not diagonalizable at all.
• Dec 3rd 2012, 11:27 PM
skhan87
Re: Finding unknown matrix
Firstly thanks for considering my querey =)

I know about enteries of X and Z and they are not equal. All (X,Y and Z) follows properties of ABCD Chain matrix.

By knowing X and Z, I reached at point where all elements of Y are giving result 0. It shouldn't be so...
• Dec 4th 2012, 12:03 AM
skhan87
Re: Finding unknown matrix
- a*((323*b)/(10000*(a*d - b*c)) - (33*d)/(250*(a*d - b*c))) - c*((173*b)/(5000*(a*d - b*c)) - (71*d)/(500*(a*d - b*c))) = 0.1324

- b*((323*b)/(10000*(a*d - b*c)) - (33*d)/(250*(a*d - b*c))) - d*((173*b)/(5000*(a*d - b*c)) - (71*d)/(500*(a*d - b*c))) = 0.0298

a*((323*a)/(10000*(a*d - b*c)) - (33*c)/(250*(a*d - b*c))) + c*((173*a)/(5000*(a*d - b*c)) - (71*c)/(500*(a*d - b*c))) = 0.1526

b*((323*a)/(10000*(a*d - b*c)) - (33*c)/(250*(a*d - b*c))) + d*((173*a)/(5000*(a*d - b*c)) - (71*c)/(500*(a*d - b*c))) = 0.0342

Here is matlab computed result. Where a,b,c and d are y11,y12,y21 and y22 respectively.
Result suppose to be a = 0.9, b=0.10, c=0.11 and d=0.12, but i couldn't reach at this point