Concept

Wronskian

Summary
In the mathematics of a square matrix, the Wronskian (or Wrońskian) is a determinant introduced by the Polish mathematician . It is used in the study of differential equations, where it can sometimes show linear independence of a set of solutions. Definition The Wronskian of two differentiable functions f  and g is W(f,g)=f g' - g f' . More generally, for n real- or complex-valued functions f1, …, fn, which are n – 1 times differentiable on an interval I, the Wronskian W(f_1,\ldots,f_n) is a function on x\in I defined by W(f_1, \ldots, f_n) (x)= \det \begin{bmatrix} f_1(x) & f_2(x) & \cdots & f_n(x) \ f_1'(x) & f_2'(x) & \cdots & f_n' (x)\ \vdots & \vdots & \ddots & \vdots \ f_1^{(n-1)}(x)& f_2^{(n-1)}(x) & \cdots & f_n^{(n-1)}(x) \end{bmatrix}. This is the determinant of the matrix constructed by placing the functions in the first row, the first derivatives of the functions in the second
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