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

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ArXiv.org
Published
2025-07-20
Primary Topic
Spectral Theory in Mathematical Physics
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article
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article

A New Generalization of the Liouville-Jacobi Identity

Lubomir Markov
ArXiv.org
Spectral Theory in Mathematical Physics
article

A New Generalization of the Liouville-Jacobi Identity

Lubomir Markov
article en

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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Spectral Theory in Mathematical Physics
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A New Generalization of the Liouville-Jacobi Identity — Lubomir Markov · ArXiv.org (2025) | TGRS Research Map | TGRS