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 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.

References in periodicals archive ?
where <y, z> := yz' - y'z is the Wronskian of y and z.
If X, Y [member of] D, then we define the Wronskian matrix of X(t) and Y(t) by
Eloe, Higher order dynamic equations on measure chains: Wronskians, disconjugacy, and interpolating families of functions, J.
21) ensures that the Wronskian matrix of the linearly independent functions ([v.
where U(t, [tau]) is the Wronskian matrix of the generating functions introduced in eq.
4) are linearly independent if and only if their Wronskian is different from zero.
i] are linearly independent over F, then there exists a generalized Wronskian of the (3), which does not vanish.
n] are linearly independent, we have there exists a generalized Wronskian W of [f.
Marini, On intermediate solutions and the Wronskian for half-linear differential equations, J.
This generalization is obtained by considering the Wronskian of functions over F[x].