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Liouville's formula

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Liouville's formula

expresses the determinant of a solution of a 1st-order system of homogeneous linear differential equations

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About Liouville's formula

In mathematics, Liouville's formula, also known as the Abel-Jacobi-Liouville Identity, is an equation 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. The formula is named after the French mathematician Joseph Liouville. Jacobi's formula provides another representation of the same mathematical relationship.

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Facts from Wikidata (CC0).