Regression problem with trace regression model

i’m working on a regression task with trace regression model that recieve as input a matrix X. 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: