Empty Set is Linearly Independent
From ProofWiki
Theorem
The empty set is a linearly independent set.
Proof
There are no sequences at all of $n$ terms of the empty set for any $n > 0$.
Hence the result holds vacuously.
$\blacksquare$
Sources
- Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 27$
