# nLab Wronskian

Given a set of $n$ functions ${f}_{1},\dots ,{f}_{n}$, one can define the matrix

$W\left({f}_{1},\dots ,{f}_{n}\right)=\left(\begin{array}{cccc}{f}_{1}& {f}_{2}& \cdots & {f}_{n}\\ {f}_{1}\prime & {f}_{2}\prime & \cdots & {f}_{n}\prime \\ \cdot & \cdot & \cdot & \cdots \\ {f}_{1}^{\left(n-1\right)}& {f}_{2}^{\left(n-1\right)}& \cdots & {f}_{n}^{\left(n-1\right)}\end{array}\right)$W(f_1,\ldots,f_n) = \left( \array{f_1 & f_2 & \cdots & f_n\\ f_1' & f_2' &\cdots & f_n'\\ \cdot &\cdot &\cdot &\cdots\\ f_1^{(n-1)} & f_2^{(n-1)} &\cdots &f_n^{(n-1)}}\right)

Wronskian is its determinant. It is used in the study of linear independence of solution of differential equations and in mathematical physics.

Created on October 10, 2011 20:59:32 by Zoran Škoda (161.53.130.104)