I read a paper and there was an equation which was finally derived an equivalent expression as

$$ L = L_{T} \otimes I_{G} + I_{T} \otimes L_{G} = {\color{blue}{L_{T} \times L_{G}}} , $$

and considering $L_{T} = U_{T}\Lambda_{T} U_{T}^{*}$ and $L_{G} = U_{G}\Lambda_{G} U_{G}^{*}$, it is obtained

$$ L = {\color{red}{(U_{T}\otimes U_{G})(\Lambda_{T} \times \Lambda_{G})(U_{T} \otimes U_{G})^*}} , $$

where $\otimes$ accounts for the Kronecker product, $*$ is the Hermitian and $\times$ is the Cartesian product.

I am confused how to obtain the results in blue and red. Would you please help me to clarify them?


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