Vector Space on Cartesian Product is Vector Space/Proof 2
Jump to navigation
Jump to search
Theorem
Let $\struct {K, +, \circ}$ be a division ring.
Let $n \in \N_{>0}$.
Let $\struct {K^n, +, \times}_K$ be the $K$-vector space $K^n$.
Then $\struct {K^n, +, \times}_K$ is a $K$-vector space.
Proof
This is a special case of a direct product of vector spaces where each of the $G_k$ is the $K$-vector space $K$.
$\blacksquare$