I'm confused by something in one of the papers I'm reading, but I'm not sure if there's any math in it that I'm not aware of.
$\mathbf{E}=\mathbf{R}\mathbf{e}$, where $\mathbf{E}\in\mathbb{C}^{n_1\times n_3}, \mathbf{R}\in\mathbb{C}^{n_1\times n_2}, \mathbf{e}\in\mathbb{C}^{n_2\times n_3}$
Currently $\mathbf{E}$ and $\mathbf{R}$ are known and it is necessary to find $\mathbf{e}$. Then the article uses the following formula to find $\mathbf{e}$
$\mathbf{R}^T\mathbf{E}=(\mathbf{R}^T\mathbf{R}+\gamma\mathbf{I})\mathbf{e}$, where $\gamma$ is the regularization factor.
I would like to know why such a transformation needs to be made and what theory it is based on. If there's any material I can reference, feel free to provide it to me. I've attached the article I'm reading, but it's in the field of computational electromagnetics.
Eqn. (2)~(3) in https://ieeexplore.ieee.org/document/10068421
Any help is appreciated.
The problem is solved.
The least-squares solution of Equation $\mathbf{E}=\mathbf{R}\mathbf{e}$ is $\mathbf{R}^T\mathbf{E}=\mathbf{R}^T\mathbf{R}\mathbf{e}$.
When the number of matrix conditions is too large, the ridge regression technique will be introduced. Therefore the $\gamma\mathbf{I}$ is added.