Definition:Linearly Dependent Real Functions

Definition
Let $\map f x$ and $\map g x$ be real functions defined on a closed interval $\closedint a b$.

Let $f$ and $g$ be constant multiples of each other:
 * $\exists c \in \R: \forall x \in \closedint a b: \map f x = c \map g x$

or:
 * $\exists c \in \R: \forall x \in \closedint a b: \map g x = c \map f x$

Then $f$ and $g$ are linearly dependent.

Also see

 * Definition:Linearly Independent Real Functions