I am writing my equation according to scenario 1 and scenario 2 and then I am trying to find a relationship between rhof2* and *rhof (or rhoM and rhom1m2)
Now, according to scenario 1, m1 and 2 are matrices which have the dimension 2*2 From scenario 1, I first write the rho_ m2 and I put rho_ m2 in the rho_f and I got this result :
rho_f1={{p_x*(p_h*rho00 + 2.0*p_h*rho11 + rho00*(1 - p_h)) +
p_x*(2.0*p_h*rho00 + 1.0*p_h*rho11 + 1.0*rho11*(1 - p_h)) +
p_x*(2.0*p_h*rho00 + p_h*rho11 + rho11*(1 - p_h)) + (1 -
p_x)*(p_h*rho00 + 2.0*p_h*rho11 + rho00*(1 - p_h)),
p_x*(p_h*rho01 - rho01*(1 - p_h)) +
p_x*(-p_h*rho10 + rho10*(1 - p_h)) +
p_x*(1.0*p_h*rho10 - 1.0*rho10*(1 - p_h)) + (1 - p_x)*(-p_h*rho01 +
rho01*(1 - p_h))}, {p_x*(-p_h*rho01 + rho01*(1 - p_h)) +
p_x*(1.0*p_h*rho01 - 1.0*rho01*(1 - p_h)) +
p_x*(p_h*rho10 - rho10*(1 - p_h)) + (1 - p_x)*(-p_h*rho10 +
rho10*(1 - p_h)),
p_x*(p_h*rho00 + 2.0*p_h*rho11 + rho00*(1 - p_h)) +
p_x*(1.0*p_h*rho00 + 2.0*p_h*rho11 + 1.0*rho00*(1 - p_h)) +
p_x*(2.0*p_h*rho00 + p_h*rho11 + rho11*(1 - p_h)) + (1 -
p_x)*(2.0*p_h*rho00 + p_h*rho11 + rho11*(1 - p_h))}}
Here p_ h is a coefficient which comes from equation of rho_ m2 and p_ x is another coefficient which comes from equation rho_f. From scenario 2, I have this equation:
rho_f2 = {{g00 . p_g + 2 . g11 . p_g + g11 . (1 - p_g), -g01 . p_g +
g10 . (1 - p_g)}, {g01 . (1 - p_g) - g10 . p_g,
2. g00 . p_g + g00 . (1 - p_g) + g11 . p_g}}
and p_g is a coeffieicent
Now I want to find a functionality/a relationship between rho and g. I want to write the g matrix in terms of rho matrix.
I tried this code(and all the combination of this code) but I am having errors:
Solve[rho_f1 . rho_f2 == {{g00, g01, g10, g11}}, Flatten[rho_f1]]
In the output it is written that:
Solve::ivar: (rho00 (1-(p:Blank[<<1>>]))+rho00 ph+2. rho11 ph) (1-px)+(rho11 (1-(p:Blank[<<1>>]))+2. rho00 ph+rho11 ph) px+(1. rho11 (1-(p:Blank[<<1>>]))+2. rho00 ph+1. rho11 ph) px+(rho00 (1-(p:Blank[<<1>>]))+rho00 ph+2. rho11 ph) px is not a valid variable.
P.S I am not even sure the solve function is the right way to do it so if you have any other suggestion, will be glad