Wronskian

Definition

Let $I$ be an interval and let $f_1, \dots, f_n : I \to \mathbb{R}$ be $n - 1$ times differentiable functions. The Wronskian of $f_1, \dots, f_n$ is the function $W(f_1, \dots, f_n) : I \to \mathbb{R}$ given by $$W(f_1, \dots, f_n)(x) = \det \begin{pmatrix} f_1(x) & f_2(x) & \cdots & f_n(x) \\ f_1'(x) & f_2'(x) & \cdots & f_n'(x) \\ \vdots & \vdots & \ddots & \vdots \\ f_1^{(n-1)}(x) & f_2^{(n-1)}(x) & \cdots & f_n^{(n-1)}(x) \end{pmatrix}.$$