\begin{definition}[Definition:Conjugate Point (Calculus of Variations)/Dependent on N Functions]
Let $K$ be a functional such that:
:$\ds K \sqbrk h = \int_a^b \paren {\mathbf h'\mathbf P \mathbf h' + \mathbf h \mathbf Q \mathbf h} \rd x$
Consider Euler's equation related to the functional $K$:
:$-\map {\dfrac \d {\d x} } {\mathbf P \mathbf h'} + \mathbf Q \mathbf h = 0$
where $\mathbf P$ and $\mathbf Q$ are symmetric matrices.
Let the general solution to this equation be:
:$\set {\mathbf h^{\paren i} = \paren {\sequence {h_{ij} } }: i,j \in \N_{\le N} }$
Let:
:$\exists j: \forall k \ne j: \paren {\map {\mathbf h^{\paren j} } a = 0} \land \paren {\map {h_{j j}'} a = 1, h'_{j k} = 0}$
Let the determinant, built from $h_{ij}$, be such that:
:$\size {h_{i j} } \paren {\tilde a} = 0$
Here $i$ denotes rows, and $j$ denotes columns.
Then $\tilde a$ is said to be '''conjugate''' to point $a$ {{WRT}} the functional $K$.
\end{definition}