Definition:Linear Differential Operator
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Definition
A linear differential operator is a differential operator $\mathscr L$ with the property that:
- $\map {\mathscr L} {\alpha \phi_1 + \beta \phi_2} = \alpha \map {\mathscr L} {\phi_1} + \beta \map {\mathscr L} {\phi_2}$
Thus if $\phi_1$ and $\phi_2$ are solutions to the differential equation $\map {\mathscr L} {\phi_i} = 0$, then so is any linear combination of $\phi_1$ and $\phi_2$.
Sources
- 1974: Robert Gilmore: Lie Groups, Lie Algebras and Some of their Applications ... (previous) ... (next): Chapter $1$: Introductory Concepts: $1$. Basic Building Blocks: $4$. LINEAR VECTOR SPACE: Example $3$