A New Generalization of the Liouville-Jacobi Identity

Lubomir Markov

A New Generalization of the Liouville-Jacobi Identity

Classical Analysis and ODEs 2025-07-22 v1

Authors: Lubomir Markov

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

Keywords

Liouville-Jacobi identity matrix differential equation determinant nonhomogeneous linear system

Cite

@article{arxiv.2507.14927,
  title  = {A New Generalization of the Liouville-Jacobi Identity},
  author = {Lubomir Markov},
  journal= {arXiv preprint arXiv:2507.14927},
  year   = {2025}
}

Comments

This result will be presented at the upcoming "Third Workshop on Soliton Theory, Nonlinear Dynamics and Machine Learning" (August 18th$-$23rd, 2025) and the subsequent paper will be submitted for publication to the {\it Journal of Physics: Conference Series

A New Generalization of the Liouville-Jacobi Identity

Abstract

Keywords

Cite

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