Number of Ordered Bases from a Basis
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Theorem
Each basis of $n$ elements determines $n!$ ordered bases.
Proof
Follows directly from Cardinality of Set of Bijections.
$\blacksquare$
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 27$. Subspaces and Bases