Wronskian


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 f1, …, fn ; ordinarily used to determine linear independence of solutions of linear homogeneous differential equations.

Wronskian

 

a functional determinant composed of n functions f1(x), f2(x)....,fn(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.