Meanings
- mathematicsAn equation, a generalization of Abel's identity, that expresses the determinant of a square-matrix solution of a first-order system of homogeneous linear differential equations in terms of the sum of the diagonal coefficients of the system.
Synonyms: Abel-Jacobi-Liouville identity
Synonyms & antonyms
proper nounAn equation, a generalization of Abel's identity, that expresses the determinant of a square-matrix solution of a first-order system of homogeneous linear differential equations in terms of the sum of the diagonal coefficients of the system.
Origin
Named after the French mathematician Joseph Liouville.
Full word history & related roots →Cite this entry
Liouville's formula. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Liouville's%20formula
“Liouville's formula.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Liouville's%20formula. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “Liouville's formula,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Liouville's%20formula.
Source: Liouville's formula on Wiktionary, CC BY-SA 4.0.