Planes are Subspaces of Space

Theorem

The two-dimensional subspaces of $\R^3$ are precisely the homogeneous planes of solid 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