Hi Dayanne,
The regulatory matrices correspond to the coefficient matrix obtained after we fit our regularized linear regression on the expression data. Each column represents the impact of a particular covariate on the expression level of each of the corresponding genes in the rows.
The magnitude in the values can roughly be interpreted using the following example m_Stat2_2 has a -1.2 impact on Rsad2 expression, since the input data was in log2, you can loosely say m_Stat2_2 reduce the amount UMIs for Rsad2 by a factor of 2.3 (for the no cells matrix).
The columns at the end represent the impact of additional covariates, which includes factors like batch, transcripts detected, or cell state.
Let me know if you have any more questions.