A New Generalization of the Liouville-Jacobi Identity
A generalized Liouville-Jacobi Identity is proved for the determinant $\det{X(t)}$ of a solution $X(t)$ to the linear nonhomogeneous first-order matrix differential equation with left- and right-coefficient matrices $\ \frac{\rm d}{{\rm d}t} X(t) + A(t)X(t) + X(t)B(t)= F(t), \ X(t_0)=X_0.$
math.CA↗