Example VSM The vector space of matrices, $M_{mn}$

Set: $M_{mn}$, the set of all matrices of size $m\times n$ and entries from $\complex{\null}$, Definition VSM.

Equality: Entry-wise, Definition ME.

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

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

Does this set with these operations fulfill the ten properties? Yes. And all we need to do is quote Theorem VSPM. Another easy one (by design).