Example VSCV The vector space $\complex{m}$

Set: $\complex{m}$, all column vectors of size $m$, Definition VSCV.

Equality: Entry-wise, Definition CVE.

Vector Addition: The “usual” addition, given in Definition CVA.

Scalar Multiplication: The “usual” scalar multiplication, given in Definition CVSM.

Does this set with these operations fulfill the ten properties? Yes. And by design all we need to do is quote Theorem VSPCV. That was easy.