I have a problem in understanding equations and try to relate it with matrix representation for programming purposes.
Could you guys explain to me the equation below?
$\Big(\sum_{\omega} \sum_{x_{s}} F^{\ast}(x_{s},\omega)^{T}F^{\ast}(x_{s},\omega)\Big)(x,x) = \sum_{\omega} \omega^{4} \sum_{x_{s}} |u(x,x_{s},\omega)|^{2}$
where $(\cdot)^{T}$ stands for transposition.
Does the functional $F^{\ast}(x_{s},\omega)$ equivalent to matrix $F^{\ast}$ with row of $x_{s}$ and column of $\omega$?
Also, does $|u(x,x_{s},\omega)|^{2}$ means $u^{T}u$?
Great thanks!