Regression problem with trace regression model

i’m new to machine learning and i’m looking for a worked example of regression problem being implemented with trace regression model which is a generalization of the well known linear regression that recieves as input a matrix X instead of vectors. It’s formula is as following:

$$y = tr(beta_*^{T} X)+ epsilon$$

where tr(·) denotes the trace, $beta$ is some unknown matrix of regression coefficients, and $epsilon$ is random noise.

Can someone with that knowledge provide me the steps to achieve the regression task where we must calculate the trace (sum of the diagonal elements) in the regression phase ? Also i need to know how to generate the regression coefficients of such matrix.

I found the description of the model here: https://arxiv.org/pdf/0912.5338.pdf