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arXiv · 2507.14927

A New Generalization of the Liouville-Jacobi Identity

Lubomir Markov
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Abstract

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 $\ \frac{{\rm d}}{{\rm d}t} X(t) + A(t)X(t) + X(t)B(t)= F(t), \ X(t_0)=X_0.$

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Lubomir Markov. 2025-07-20. A New Generalization of the Liouville-Jacobi Identity. https://arxiv.org/abs/2507.14927

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