Empty Set is Linearly Independent
Jump to navigation
Jump to search
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
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 27$. Subspaces and Bases