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

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.15$: The General Solution of the Homogeneous Equation