Definition:Linearly Dependent Real Functions
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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
Sources
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.15$: The General Solution of the Homogeneous Equation