I have been trying to simplify this matrix $$ \left( \begin{array}{cc} \frac{1}{2} \left(-2 g \sqrt{1-\text{tauA}} \sqrt{1-\text{tauB}}+\text{mu} \text{tauA}+\text{mu} \text{tauB}+\text{omegaA} (1-\text{tauA})+\text{omegaB} (1-\text{tauB})\right) & 0 \\ 0 & \frac{1}{2} \left(2 \text{gprime} \sqrt{1-\text{tauA}} \sqrt{1-\text{tauB}}+\text{mu} \text{tauA}+\text{mu} \text{tauB}+\text{omegaA} (1-\text{tauA})+\text{omegaB} (1-\text{tauB})\right) \\ \end{array} \right) $$
using the following algebraic substitutions $$ omegaA - omegaA \cdot tauA + omegaB - omegaB \cdot tauB \to kappa $$
$$ 2 \sqrt{(1 - tauA)(1 - tauB)} \to u $$
I've tried a few options, but none of them seem to work. I've tried
theta /. {omegaA - omegaA*tauA + omegaB - omegaB*tauB -> kappa,
2* Sqrt[(1 - tauA)]*Sqrt[(1 - tauB)] -> u}
But this doesn't seem to do anything. I've also tried
Simplify[theta, {omegaA - omegaA*tauA + omegaB - omegaB*tauB == kappa,
2 Sqrt[(1 - tauA) (1 - tauB)] == u}]
But for some reason this only works for substituting kappa and I get
{{1/2 (kappa - 2 g Sqrt[(-1 + tauA) (-1 + tauB)] + mu (tauA + tauB)),
0}, {0, 1/
2 (kappa + 2 gprime Sqrt[(-1 + tauA) (-1 + tauB)] +
mu (tauA + tauB))}}
Can anyone explain why I'm having trouble with getting this to work? I know I could just replace the expressions by hand, but I'd really like to understand why this isn't working. Any help would be greatly appreciated.
