# Wronskian

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## Wronskian

[′vrän·skē·ən] (mathematics)

An

*n*×*n*matrix whose*i*th row is a list of the (*i*- 1)st derivatives of a set of functions*f*_{1}, …,*f*_{n }; ordinarily used to determine linear independence of solutions of linear homogeneous differential equations.## Wronskian

a functional determinant composed of *n* functions f_{1}(x), f_{2}(x)....,f_{n}(x) and their derivatives up to the order *n* - 1 inclusive:

The vanishment of the Wrońskian *[W(x) =* 0] is a necessary and, under certain additional assumptions, a sufficient condition for the linear dependence between the given *n* functions, differentiated *n -* 1 times. Based on this, the Wrońskian is used in the theory of linear differential equations. The Wrońskian was introduced by J. Wroński in 1812.