Lines are Subspaces of Plane
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Theorem
The one-dimensional subspaces of $\R^2$ are precisely the homogeneous lines of plane analytic geometry.
Proof
Follows directly from Equivalent Statements for Vector Subspace Dimension One Less.
$\blacksquare$
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Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 28$. Linear Transformations